OCME · Bilingual mathematics & derivations
From Natural Numbers to Absolute Value on the Real Line
Move from natural numbers used for counting to integers and rational numbers, enter the real-number system through completion language, and then express number-line distance with absolute value.
This is a suggested learning sequence, not a universal logical dependency or a formal proof.
Natural number
Begin by fixing the convention for natural numbers and zero.
Integer
Add a negative direction to form the integers.
Rational number
Represent rational numbers as ratios of two integers while excluding a zero denominator.
Real number
Enter the real-number system through the rational embedding and completion.
Absolute value
Use a piecewise function to express the nonnegative distance from a real number to zero.
Path source & status
path-number-system-extension-candidate · candidate