# Re: The seven step-Mathematical preliminaries

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On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:```
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>
> Bruno Marchal skrev:
>> 4) The set of all natural numbers. This set is hard to define, yet I
>> hope you agree we can describe it by the infinite quasi exhaustion by
>> {0, 1, 2, 3, ...}.
>>
>
> Let N be the biggest number in the set {0, 1, 2, 3, ...}.
>
> Exercise: does the number N+1 belongs to the set of natural numbers,
> that is does N+1 belongs to {0, 1, 2, 3, ...}?

Yes. N+1 belongs to {0, 1, 2, 3, ...}.
This follows from classical logic and the fact that the proposition "N
be the biggest number in the set {0, 1, 2, 3, ...}" is always false.
And false implies all propositions.

But this is a bit advanced matter, Torgny. The math I am explaining to
Kim and some others are typical classical mathematics.

Bruno

http://iridia.ulb.ac.be/~marchal/

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