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, …

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 …

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 …

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 …

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

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 …

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 …

Recently, sources for mathematical infotainment, for example numberphile, have given some information on the interpretation of divergent series as real numbers, for example …

Jan 12, 2018 · I remember reading a simple proof that natural numbers are infinite which goes like the following: Let $ℕ$ be the set of natural numbers. Assume that $ℕ$ is finite. Now consider …

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 $.