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RolyPoly
 2 years ago
Whether zero is a natural number or not is still controversial.
What is the (mathematical) argument for 0 *NOT* being a natural number?
RolyPoly
 2 years ago
Whether zero is a natural number or not is still controversial. What is the (mathematical) argument for 0 *NOT* being a natural number?

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Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1Have you read http://math.stackexchange.com/questions/283/is0anaturalnumber already?

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1My argument for \(0 \notin \mathbb{N}\) is simply because I find it more handy to deal with the notations this way, take for example the notation of a limit of a sequence \(a_n\): \[\Large \forall \epsilon > 0, \exists N \in \mathbb{N} \text{ such that } \forall n \geq N, a_na < \epsilon \] If you would define \(\mathbb{N}={0,1,2, \dots } \) then the above notation would require a slight update because \(N\) should be a positive number, whereas \(0\) accounts for a neutral number.

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0"In mathematics, there are two conventions for the set of natural numbers: it is either the set of positive integers {1,2,3,…} according to the traditional definition;" What is that traditional definition?

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1positive integers is the traditional definition, 1,2,3,4,5,... also known as counting numbers, because it is how we traditionally count. While 0,1,2,3,4... are considered as integers including 0 which apparently came up in the 19th century.

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0How do you define "positive integers"?

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1positive integers \( \lbrace n \in \mathbb{Z} \mid n > 0 \rbrace= 1,2,3,4, \dots \)

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1where \(\mathbb{Z}=\lbrace...,3,2,1,0,1,2,3,\dots \rbrace \)

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0Alright, thanks a lot for your help!
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