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Topic: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Replies: 3   Last Post: Oct 1, 2017 11:08 PM

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Registered: 12/12/04
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Oct 1, 2017 11:08 PM
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On Sunday, October 1, 2017 at 1:32:32 PM UTC-6, John Gabriel wrote:

> Peano's Crapaxiom 5 is the induction axiom:

> If a set S of numbers contains zero and also the successor of every
> number in S, then every number is in S.

Well, that's clearly wrong. 1/2 would not be in S, and we're all agreed
that 1/2 is a number.

However, I think this is really what Peano was saying:

If S contains zero,
and if it is also true that
if S contains x then it contains the successor of x

(where the successor of x is what we would normally call x+1, but Peano hadn't gotten around to defining addition yet)

then S will contain 0, 1, 2, 3, 4, 5... and indeed any non-negative integer.

For example, it contains 5 because

S contained zero
and because if it contains x, it contains x+1,
it contains 1 because it contains 0
it contains 2 because it contains 1
it contains 3 because it contains 2
it contains 4 because it contains 3
it contains 5 because it contains 4

Clearly, this will work for any non-negative integer, however large,
even if one doesn't bother to type that much.

John Savard

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