From the Wikipedia article: In mathematics, there are two conventions for the set of natural numbers: it is either the set of positive integers $\ {1, 2, 3, \dots\}$ according to the traditional definition; or the …

What are the natural numbers? Is it a valid question at all? My understanding is that a set satisfying Peano axioms is called "the natural numbers" and from that one builds integers, rational numb...

Sep 21, 2017 · That being said, this "inductive set" definition of the natural numbers comes from a book on analysis, not axiomatic set theory. The goal of the book is to do real analysis (i.e. to study limits, …

Apr 5, 2015 · The natural numbers have different definitions depending on the book; sometimes the natural numbers are just the positive integers $\mathbb N=\mathbb Z^+$, but other times the natural …

Jan 8, 2015 · The natural numbers are those we use for counting objects. Some authors include $0$ as a 'natural' number of objects to have and some don't. There is no consensus in the mathematical …

In mathematics, there seem to be a lot of different types of numbers. What exactly are: Real numbers Integers Rational numbers Decimals Complex numbers Natural numbers Cardinals Ordinals And as …

You can't seriously believe there are only finitely many numbers. "If a natural is finite, then that natural plus one is finite, hence the set of all naturals is finite" - this is a non sequitor, the set of all naturals is …

Even though there appears to be some confusion as to exactly What are the "whole numbers"?, my question is what is the symbol to represent the set $0, 1, 2, \ldots $.

Recently, sources for mathematical infotainment, for example numberphile, have given some information on the interpretation of divergent series as real numbers, for example $\\sum_{i=0}^\\infty i = ...

6 When one subtracts a natural number from another, say $1-2=-1$, one may not get a natural number. However, this does not forbid us from defining substraction. Substraction would be closed if we …