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

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Spacelimbus Group TitleBest ResponseYou've already chosen the best response.1
Have you read http://math.stackexchange.com/questions/283/is0anaturalnumber already?
 6 months ago

Spacelimbus Group TitleBest ResponseYou've already chosen the best response.1
My 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.
 6 months ago

RolyPoly Group TitleBest 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?
 6 months ago

Spacelimbus Group TitleBest ResponseYou've already chosen the best response.1
positive 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.
 6 months ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.0
How do you define "positive integers"?
 6 months ago

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

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

RolyPoly Group TitleBest ResponseYou've already chosen the best response.0
Alright, thanks a lot for your help!
 6 months ago
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