Bijectivity Foundations

Yes

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is Yes.

Yes

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is Yes.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

Yes

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is Yes.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

Yes

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is Yes.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

Yes

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is Yes.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

Yes

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is Yes.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

Yes

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is Yes.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

No

Both conditions must hold, equivalently every codomain target must have exactly one permitted preimage. The answer is No.

bijective

Check distinct-input collisions and full codomain coverage separately; their two truth values give bijective. Set sizes alone do not classify this supplied function.

bijective

Check distinct-input collisions and full codomain coverage separately; their two truth values give bijective. Set sizes alone do not classify this supplied function.

injective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give injective only. Set sizes alone do not classify this supplied function.

surjective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give surjective only. Set sizes alone do not classify this supplied function.

neither injective nor surjective

Check distinct-input collisions and full codomain coverage separately; their two truth values give neither injective nor surjective. Set sizes alone do not classify this supplied function.

bijective

Check distinct-input collisions and full codomain coverage separately; their two truth values give bijective. Set sizes alone do not classify this supplied function.

injective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give injective only. Set sizes alone do not classify this supplied function.

surjective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give surjective only. Set sizes alone do not classify this supplied function.

neither injective nor surjective

Check distinct-input collisions and full codomain coverage separately; their two truth values give neither injective nor surjective. Set sizes alone do not classify this supplied function.

bijective

Check distinct-input collisions and full codomain coverage separately; their two truth values give bijective. Set sizes alone do not classify this supplied function.

injective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give injective only. Set sizes alone do not classify this supplied function.

surjective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give surjective only. Set sizes alone do not classify this supplied function.

neither injective nor surjective

Check distinct-input collisions and full codomain coverage separately; their two truth values give neither injective nor surjective. Set sizes alone do not classify this supplied function.

bijective

Check distinct-input collisions and full codomain coverage separately; their two truth values give bijective. Set sizes alone do not classify this supplied function.

injective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give injective only. Set sizes alone do not classify this supplied function.

surjective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give surjective only. Set sizes alone do not classify this supplied function.

neither injective nor surjective

Check distinct-input collisions and full codomain coverage separately; their two truth values give neither injective nor surjective. Set sizes alone do not classify this supplied function.

bijective

Check distinct-input collisions and full codomain coverage separately; their two truth values give bijective. Set sizes alone do not classify this supplied function.

injective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give injective only. Set sizes alone do not classify this supplied function.

surjective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give surjective only. Set sizes alone do not classify this supplied function.

neither injective nor surjective

Check distinct-input collisions and full codomain coverage separately; their two truth values give neither injective nor surjective. Set sizes alone do not classify this supplied function.

bijective

Check distinct-input collisions and full codomain coverage separately; their two truth values give bijective. Set sizes alone do not classify this supplied function.

injective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give injective only. Set sizes alone do not classify this supplied function.

surjective only

Check distinct-input collisions and full codomain coverage separately; their two truth values give surjective only. Set sizes alone do not classify this supplied function.

neither injective nor surjective

Check distinct-input collisions and full codomain coverage separately; their two truth values give neither injective nor surjective. Set sizes alone do not classify this supplied function.

∅

Count the permitted preimages of every element of B to obtain ∅. The profile includes zero-size fibers, not only attained targets.

{(0, 1), (1, 1)}

Count the permitted preimages of every element of B to obtain {(0, 1), (1, 1)}. The profile includes zero-size fibers, not only attained targets.

{(1, 1), (3, 1), (5, 0)}

Count the permitted preimages of every element of B to obtain {(1, 1), (3, 1), (5, 0)}. The profile includes zero-size fibers, not only attained targets.

{(0, 2)}

Count the permitted preimages of every element of B to obtain {(0, 2)}. The profile includes zero-size fibers, not only attained targets.

{(-3, 0), (-2, 0), (-1, 2)}

Count the permitted preimages of every element of B to obtain {(-3, 0), (-2, 0), (-1, 2)}. The profile includes zero-size fibers, not only attained targets.

{(0, 1), (1, 1), (2, 1)}

Count the permitted preimages of every element of B to obtain {(0, 1), (1, 1), (2, 1)}. The profile includes zero-size fibers, not only attained targets.

{(1, 1), (3, 1), (5, 1), (7, 0)}

Count the permitted preimages of every element of B to obtain {(1, 1), (3, 1), (5, 1), (7, 0)}. The profile includes zero-size fibers, not only attained targets.

{(0, 2), (1, 1)}

Count the permitted preimages of every element of B to obtain {(0, 2), (1, 1)}. The profile includes zero-size fibers, not only attained targets.

{(-4, 0), (-3, 0), (-2, 1), (-1, 2)}

Count the permitted preimages of every element of B to obtain {(-4, 0), (-3, 0), (-2, 1), (-1, 2)}. The profile includes zero-size fibers, not only attained targets.

{(0, 1), (1, 1), (2, 1), (3, 1)}

Count the permitted preimages of every element of B to obtain {(0, 1), (1, 1), (2, 1), (3, 1)}. The profile includes zero-size fibers, not only attained targets.

{(1, 1), (3, 1), (5, 1), (7, 1), (9, 0)}

Count the permitted preimages of every element of B to obtain {(1, 1), (3, 1), (5, 1), (7, 1), (9, 0)}. The profile includes zero-size fibers, not only attained targets.

{(0, 2), (1, 1), (2, 1)}

Count the permitted preimages of every element of B to obtain {(0, 2), (1, 1), (2, 1)}. The profile includes zero-size fibers, not only attained targets.

{(-5, 0), (-4, 0), (-3, 0), (-2, 2), (-1, 2)}

Count the permitted preimages of every element of B to obtain {(-5, 0), (-4, 0), (-3, 0), (-2, 2), (-1, 2)}. The profile includes zero-size fibers, not only attained targets.

{(0, 1), (1, 1), (2, 1), (3, 1), (4, 1)}

Count the permitted preimages of every element of B to obtain {(0, 1), (1, 1), (2, 1), (3, 1), (4, 1)}. The profile includes zero-size fibers, not only attained targets.

{(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 0)}

Count the permitted preimages of every element of B to obtain {(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 0)}. The profile includes zero-size fibers, not only attained targets.

{(0, 2), (1, 1), (2, 1), (3, 1)}

Count the permitted preimages of every element of B to obtain {(0, 2), (1, 1), (2, 1), (3, 1)}. The profile includes zero-size fibers, not only attained targets.

{(-6, 0), (-5, 0), (-4, 0), (-3, 1), (-2, 2), (-1, 2)}

Count the permitted preimages of every element of B to obtain {(-6, 0), (-5, 0), (-4, 0), (-3, 1), (-2, 2), (-1, 2)}. The profile includes zero-size fibers, not only attained targets.

{(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1)}

Count the permitted preimages of every element of B to obtain {(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1)}. The profile includes zero-size fibers, not only attained targets.

{(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 1), (13, 0)}

Count the permitted preimages of every element of B to obtain {(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 1), (13, 0)}. The profile includes zero-size fibers, not only attained targets.

{(0, 2), (1, 1), (2, 1), (3, 1), (4, 1)}

Count the permitted preimages of every element of B to obtain {(0, 2), (1, 1), (2, 1), (3, 1), (4, 1)}. The profile includes zero-size fibers, not only attained targets.

{(-7, 0), (-6, 0), (-5, 0), (-4, 0), (-3, 2), (-2, 2), (-1, 2)}

Count the permitted preimages of every element of B to obtain {(-7, 0), (-6, 0), (-5, 0), (-4, 0), (-3, 2), (-2, 2), (-1, 2)}. The profile includes zero-size fibers, not only attained targets.

{(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}

Count the permitted preimages of every element of B to obtain {(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}. The profile includes zero-size fibers, not only attained targets.

{(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 1), (13, 1), (15, 0)}

Count the permitted preimages of every element of B to obtain {(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 1), (13, 1), (15, 0)}. The profile includes zero-size fibers, not only attained targets.

{(0, 2), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1)}

Count the permitted preimages of every element of B to obtain {(0, 2), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1)}. The profile includes zero-size fibers, not only attained targets.

{(-8, 0), (-7, 0), (-6, 0), (-5, 0), (-4, 1), (-3, 2), (-2, 2), (-1, 2)}

Count the permitted preimages of every element of B to obtain {(-8, 0), (-7, 0), (-6, 0), (-5, 0), (-4, 1), (-3, 2), (-2, 2), (-1, 2)}. The profile includes zero-size fibers, not only attained targets.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

No

Finite sets admit a bijection exactly when their cardinalities agree, giving No. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.

Yes

Finite sets admit a bijection exactly when their cardinalities agree, giving Yes. This asks about existence rather than testing a given function; two empty sets admit the unique empty bijection.