Is $0$ a natural number? - Mathematics Stack Exchange
194 Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was …
Why do some accept zero as a natural number but others don't?
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 …
analysis - Is $0$ the only natural number which does not have a ...
Jan 3, 2025 · Axiom 2.3 guarantees that zero is not the successor of any natural number. But it doesn't guarantee its uniqueness thus there can exist some other natural number $\alpha$ such that it is not …
0 as an element of the natural numbers [duplicate]
Apr 10, 2015 · Some advantages of considering 0 to be a natural number: The starting point for set theory is the empty set. The number n can be identified as the set of the first n natural numbers …
What is a natural number? - Mathematics Stack Exchange
Sep 21, 2017 · There are a number of reasons why an exposition of real analysis might construct the natural numbers from the real numbers; the two most prominent are: It is technically convenient to …
Why do some people state that 'Zero is not a number'?
A few distinctions: In your first link, the discussion is regarding whether $0$ is a natural number, not that it is/isn't a number. Your second link is predicated upon fairly weak, insubstantial first-year …
What are the pros/cons of the Natural numbers including 0?
Feb 25, 2020 · Example: if $0 \notin \mathbb N$, then the precise statement about finite dimensional vector spaces becomes "the dimension of a finite-dimensional vector space is a natural number or …
Why does Shilov exclude $0$ from natural numbers?
Sep 6, 2023 · The author just arbitrarily began with defining naturals as $1,1+1,1+1+1,\dots$ (as is his right) but there is no good justification for why he made that choice beyond that it was convenient for …
soft question - Is zero irrational? - Mathematics Stack Exchange
One perspective on this is to regard $0$ as a symbol that actually refers to several different mathematical objects: $0$-the-natural-number, usually the first natural number defined. Let's write …
Set of natural numbers and Peano axioms - Mathematics Stack Exchange
Feb 2, 2021 · Each natural number is defined to be the successor the the previous number. In other words, Only the number zero is initially given and all of the rest of the natural numbers are …