lpetrich
Contributor
What is a natural number? A whole number? An integer?
I've discovered:
For counting, we always use positive integers: 1, 2, 3, 4, 5, ...
But for set theory, we also need zero, giving the nonnegative integers: 0, 1, 2, 3, 4, 5, ...
One also needs zero to get addition and multiplication in a straightforward way from Peano's axioms of arithmetic. Those axioms define natural numbers from some initial number and a successor for each number.
As to the word "integer", it comes from Latin "integer" and I find
integer - Wiktionary - Latin adjective
So "integer" is from a word that means "whole".
I've discovered:
- Natural number: positive integer, nonnegative integer
- Whole number: positive integer, nonnegative integer, integer
For counting, we always use positive integers: 1, 2, 3, 4, 5, ...
But for set theory, we also need zero, giving the nonnegative integers: 0, 1, 2, 3, 4, 5, ...
One also needs zero to get addition and multiplication in a straightforward way from Peano's axioms of arithmetic. Those axioms define natural numbers from some initial number and a successor for each number.
As to the word "integer", it comes from Latin "integer" and I find
integer - Wiktionary - Latin adjective
- complete, whole, intact
- uninjured, sound, healthy
So "integer" is from a word that means "whole".