# Real Order Foundations

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261005-advance-20261006-r01-order-relation-foundations · 2026-10-05 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (0)/1 and (0)/1. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation=

The exact cross products are 0 and 0, giving =. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0001/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 2. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-2)/3 and (-9)/2. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are -4 and -27, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0002/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 3. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (3)/4 and (-8)/3. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are 9 and -32, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0003/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 4. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-4)/5 and (-5)/4. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are -16 and -25, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0004/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 5. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (5)/6 and (-6)/1. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are 5 and -36, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0005/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 6. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-6)/2 and (-5)/2. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation<

The exact cross products are -12 and -10, giving <. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0006/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 7. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (7)/3 and (7)/3. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation=

The exact cross products are 21 and 21, giving =. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0007/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 8. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-8)/4 and (-3)/4. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation<

The exact cross products are -32 and -12, giving <. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0008/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 9. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (9)/5 and (-2)/1. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are 9 and -10, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0009/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 10. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-10)/6 and (-11)/2. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are -20 and -66, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0010/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 11. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (11)/2 and (0)/3. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are 33 and 0, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0011/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 12. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-12)/3 and (1)/4. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation<

The exact cross products are -48 and 3, giving <. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0012/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 13. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (13)/4 and (13)/4. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation=

The exact cross products are 52 and 52, giving =. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0013/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 14. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-14)/5 and (3)/2. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation<

The exact cross products are -28 and 15, giving <. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0014/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 15. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (15)/6 and (4)/3. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are 45 and 24, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0015/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 16. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-16)/2 and (-17)/4. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation<

The exact cross products are -64 and -34, giving <. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0016/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 17. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (17)/3 and (6)/1. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation<

The exact cross products are 17 and 18, giving <. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0017/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 18. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-18)/4 and (7)/2. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation<

The exact cross products are -36 and 28, giving <. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0018/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 19. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (19)/5 and (19)/5. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation=

The exact cross products are 95 and 95, giving =. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0019/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 20. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-20)/6 and (9)/4. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation<

The exact cross products are -80 and 54, giving <. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0020/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 21. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (21)/2 and (10)/1. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are 21 and 20, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0021/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 22. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-22)/3 and (-23)/2. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are -44 and -69, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0022/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 23. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (23)/4 and (12)/3. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation>

The exact cross products are 69 and 48, giving >. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0023/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 24. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (-24)/5 and (13)/4. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation<

The exact cross products are -96 and 65, giving <. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0024/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 25. Exact Order of Positive-Denominator Rationals

Under the usual real order, compare (25)/6 and (25)/6. Both denominators are positive. Give <, =, or > in that order.

View answer and explanation=

The exact cross products are 150 and 150, giving =. Positive denominators preserve the comparison direction.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0025/)

Usual order on the real numbers · qf-order-rational-comparison · candidate





## 26. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {0}. Give (minimum, maximum).

View answer and explanation(0, 0)

Order the given elements to obtain (0, 0). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0026/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 27. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-1, 0, 3}. Give (minimum, maximum).

View answer and explanation(-1, 3)

Order the given elements to obtain (-1, 3). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0027/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 28. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-2, 0, 4}. Give (minimum, maximum).

View answer and explanation(-2, 4)

Order the given elements to obtain (-2, 4). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0028/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 29. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-3, 0, 5}. Give (minimum, maximum).

View answer and explanation(-3, 5)

Order the given elements to obtain (-3, 5). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0029/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 30. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-7, -6, -4}. Give (minimum, maximum).

View answer and explanation(-7, -4)

Order the given elements to obtain (-7, -4). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0030/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 31. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-5, 0, 7}. Give (minimum, maximum).

View answer and explanation(-5, 7)

Order the given elements to obtain (-5, 7). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0031/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 32. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-6, 0, 8}. Give (minimum, maximum).

View answer and explanation(-6, 8)

Order the given elements to obtain (-6, 8). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0032/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 33. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-7, 0, 9}. Give (minimum, maximum).

View answer and explanation(-7, 9)

Order the given elements to obtain (-7, 9). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0033/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 34. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-11, -10, -8}. Give (minimum, maximum).

View answer and explanation(-11, -8)

Order the given elements to obtain (-11, -8). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0034/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 35. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-9, 0, 11}. Give (minimum, maximum).

View answer and explanation(-9, 11)

Order the given elements to obtain (-9, 11). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0035/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 36. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-10, 0, 12}. Give (minimum, maximum).

View answer and explanation(-10, 12)

Order the given elements to obtain (-10, 12). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0036/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 37. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-11, 0, 13}. Give (minimum, maximum).

View answer and explanation(-11, 13)

Order the given elements to obtain (-11, 13). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0037/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 38. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-15, -14, -12}. Give (minimum, maximum).

View answer and explanation(-15, -12)

Order the given elements to obtain (-15, -12). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0038/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 39. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-13, 0, 15}. Give (minimum, maximum).

View answer and explanation(-13, 15)

Order the given elements to obtain (-13, 15). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0039/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 40. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-14, 0, 16}. Give (minimum, maximum).

View answer and explanation(-14, 16)

Order the given elements to obtain (-14, 16). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0040/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 41. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-15, 0, 17}. Give (minimum, maximum).

View answer and explanation(-15, 17)

Order the given elements to obtain (-15, 17). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0041/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 42. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-19, -18, -16}. Give (minimum, maximum).

View answer and explanation(-19, -16)

Order the given elements to obtain (-19, -16). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0042/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 43. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-17, 0, 19}. Give (minimum, maximum).

View answer and explanation(-17, 19)

Order the given elements to obtain (-17, 19). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0043/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 44. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-18, 0, 20}. Give (minimum, maximum).

View answer and explanation(-18, 20)

Order the given elements to obtain (-18, 20). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0044/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 45. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-19, 0, 21}. Give (minimum, maximum).

View answer and explanation(-19, 21)

Order the given elements to obtain (-19, 21). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0045/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 46. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-23, -22, -20}. Give (minimum, maximum).

View answer and explanation(-23, -20)

Order the given elements to obtain (-23, -20). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0046/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 47. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-21, 0, 23}. Give (minimum, maximum).

View answer and explanation(-21, 23)

Order the given elements to obtain (-21, 23). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0047/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 48. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-22, 0, 24}. Give (minimum, maximum).

View answer and explanation(-22, 24)

Order the given elements to obtain (-22, 24). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0048/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 49. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-23, 0, 25}. Give (minimum, maximum).

View answer and explanation(-23, 25)

Order the given elements to obtain (-23, 25). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0049/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 50. Minimum and Maximum of a Finite Real Set

Under the usual real order, the explicit finite nonempty set has elements {-27, -26, -24}. Give (minimum, maximum).

View answer and explanation(-27, -24)

Order the given elements to obtain (-27, -24). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0050/)

Usual order on the real numbers · qf-order-finite-extrema · candidate





## 51. Membership Including Closed Endpoints

Under the usual real order, is (0)/1 in the closed interval [0, 0]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check 0·1≤0≤0·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0051/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 52. Membership Including Closed Endpoints

Under the usual real order, is (6)/2 in the closed interval [-1, 3]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -1·2≤6≤3·2 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0052/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 53. Membership Including Closed Endpoints

Under the usual real order, is (-7)/3 in the closed interval [-2, 4]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -2·3≤-7≤4·3 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0053/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 54. Membership Including Closed Endpoints

Under the usual real order, is (21)/4 in the closed interval [-3, 5]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -3·4≤21≤5·4 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0054/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 55. Membership Including Closed Endpoints

Under the usual real order, is (1)/1 in the closed interval [-4, 6]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -4·1≤1≤6·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0055/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 56. Membership Including Closed Endpoints

Under the usual real order, is (-10)/2 in the closed interval [-5, 7]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -5·2≤-10≤7·2 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0056/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 57. Membership Including Closed Endpoints

Under the usual real order, is (24)/3 in the closed interval [-6, 8]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -6·3≤24≤8·3 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0057/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 58. Membership Including Closed Endpoints

Under the usual real order, is (-29)/4 in the closed interval [-7, 9]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -7·4≤-29≤9·4 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0058/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 59. Membership Including Closed Endpoints

Under the usual real order, is (11)/1 in the closed interval [-8, 10]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -8·1≤11≤10·1 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0059/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 60. Membership Including Closed Endpoints

Under the usual real order, is (1)/2 in the closed interval [-9, 11]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -9·2≤1≤11·2 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0060/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 61. Membership Including Closed Endpoints

Under the usual real order, is (-30)/3 in the closed interval [-10, 12]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -10·3≤-30≤12·3 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0061/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 62. Membership Including Closed Endpoints

Under the usual real order, is (52)/4 in the closed interval [-11, 13]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -11·4≤52≤13·4 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0062/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 63. Membership Including Closed Endpoints

Under the usual real order, is (-13)/1 in the closed interval [-12, 14]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -12·1≤-13≤14·1 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0063/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 64. Membership Including Closed Endpoints

Under the usual real order, is (31)/2 in the closed interval [-13, 15]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -13·2≤31≤15·2 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0064/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 65. Membership Including Closed Endpoints

Under the usual real order, is (1)/3 in the closed interval [-14, 16]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -14·3≤1≤16·3 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0065/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 66. Membership Including Closed Endpoints

Under the usual real order, is (-60)/4 in the closed interval [-15, 17]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -15·4≤-60≤17·4 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0066/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 67. Membership Including Closed Endpoints

Under the usual real order, is (18)/1 in the closed interval [-16, 18]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -16·1≤18≤18·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0067/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 68. Membership Including Closed Endpoints

Under the usual real order, is (-35)/2 in the closed interval [-17, 19]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -17·2≤-35≤19·2 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0068/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 69. Membership Including Closed Endpoints

Under the usual real order, is (61)/3 in the closed interval [-18, 20]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -18·3≤61≤20·3 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0069/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 70. Membership Including Closed Endpoints

Under the usual real order, is (1)/4 in the closed interval [-19, 21]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -19·4≤1≤21·4 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0070/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 71. Membership Including Closed Endpoints

Under the usual real order, is (-20)/1 in the closed interval [-20, 22]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -20·1≤-20≤22·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0071/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 72. Membership Including Closed Endpoints

Under the usual real order, is (46)/2 in the closed interval [-21, 23]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -21·2≤46≤23·2 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0072/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 73. Membership Including Closed Endpoints

Under the usual real order, is (-67)/3 in the closed interval [-22, 24]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -22·3≤-67≤24·3 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0073/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 74. Membership Including Closed Endpoints

Under the usual real order, is (101)/4 in the closed interval [-23, 25]? The denominator is positive and both endpoints are included.

View answer and explanationNo

Check -23·4≤101≤25·4 exactly, obtaining No. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0074/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 75. Membership Including Closed Endpoints

Under the usual real order, is (1)/1 in the closed interval [-24, 26]? The denominator is positive and both endpoints are included.

View answer and explanationYes

Check -24·1≤1≤26·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0075/)

Usual order on the real numbers · qf-order-closed-interval · candidate





## 76. Order after a Common Addend

Under the usual real order, a=0, b=0, and c=-12. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation=

The translated values are -12 and -12, with relation =. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0076/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 77. Order after a Common Addend

Under the usual real order, a=-3, b=2, and c=-11. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation<

The translated values are -14 and -9, with relation <. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0077/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 78. Order after a Common Addend

Under the usual real order, a=-4, b=-8, and c=-10. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation>

The translated values are -14 and -18, with relation >. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0078/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 79. Order after a Common Addend

Under the usual real order, a=-5, b=-5, and c=-9. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation=

The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0079/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 80. Order after a Common Addend

Under the usual real order, a=-6, b=5, and c=-8. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation<

The translated values are -14 and -3, with relation <. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0080/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 81. Order after a Common Addend

Under the usual real order, a=-7, b=-14, and c=-7. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation>

The translated values are -14 and -21, with relation >. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0081/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 82. Order after a Common Addend

Under the usual real order, a=-8, b=-8, and c=-6. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation=

The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0082/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 83. Order after a Common Addend

Under the usual real order, a=-9, b=8, and c=-5. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation<

The translated values are -14 and 3, with relation <. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0083/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 84. Order after a Common Addend

Under the usual real order, a=-10, b=-20, and c=-4. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation>

The translated values are -14 and -24, with relation >. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0084/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 85. Order after a Common Addend

Under the usual real order, a=-11, b=-11, and c=-3. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation=

The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0085/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 86. Order after a Common Addend

Under the usual real order, a=-12, b=11, and c=-2. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation<

The translated values are -14 and 9, with relation <. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0086/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 87. Order after a Common Addend

Under the usual real order, a=-13, b=-26, and c=-1. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation>

The translated values are -14 and -27, with relation >. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0087/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 88. Order after a Common Addend

Under the usual real order, a=-14, b=-14, and c=0. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation=

The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0088/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 89. Order after a Common Addend

Under the usual real order, a=-15, b=14, and c=1. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation<

The translated values are -14 and 15, with relation <. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0089/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 90. Order after a Common Addend

Under the usual real order, a=-16, b=-32, and c=2. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation>

The translated values are -14 and -30, with relation >. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0090/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 91. Order after a Common Addend

Under the usual real order, a=-17, b=-17, and c=3. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation=

The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0091/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 92. Order after a Common Addend

Under the usual real order, a=-18, b=17, and c=4. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation<

The translated values are -14 and 21, with relation <. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0092/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 93. Order after a Common Addend

Under the usual real order, a=-19, b=-38, and c=5. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation>

The translated values are -14 and -33, with relation >. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0093/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 94. Order after a Common Addend

Under the usual real order, a=-20, b=-20, and c=6. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation=

The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0094/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 95. Order after a Common Addend

Under the usual real order, a=-21, b=20, and c=7. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation<

The translated values are -14 and 27, with relation <. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0095/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 96. Order after a Common Addend

Under the usual real order, a=-22, b=-44, and c=8. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation>

The translated values are -14 and -36, with relation >. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0096/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 97. Order after a Common Addend

Under the usual real order, a=-23, b=-23, and c=9. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation=

The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0097/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 98. Order after a Common Addend

Under the usual real order, a=-24, b=23, and c=10. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation<

The translated values are -14 and 33, with relation <. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0098/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 99. Order after a Common Addend

Under the usual real order, a=-25, b=-50, and c=11. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation>

The translated values are -14 and -39, with relation >. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0099/)

Usual order on the real numbers · qf-order-common-translation · candidate





## 100. Order after a Common Addend

Under the usual real order, a=-26, b=-26, and c=12. Compare a+c and b+c, giving <, =, or > in that order.

View answer and explanation=

The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r01-order-relation-0100/)

Usual order on the real numbers · qf-order-common-translation · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261005-advance-20261006-r01-order-relation-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261005-advance-20261006-r01-order-relation-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261005-advance-20261006-r01-order-relation-foundations/validation-report.json)