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Topic: A more stupid Italian mythmatician exists? Peano was a moron of
galactic proportions.

Replies: 10   Last Post: Oct 3, 2017 12:36 PM

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Me

Posts: 1,386
Registered: 1/23/16
Re: A more stupid Italian mythmatician exists? Peano was a moron of
galactic proportions.

Posted: Sep 30, 2017 9:53 AM
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On Saturday, September 30, 2017 at 3:36:34 PM UTC+2, Me wrote:

> I can show you one:

A variant. (I guess it will work, but didn't check it in detail.)

> Let n, m e IN. [Where IN is defined due to von Neumann.]
>
> Then
>
> n + m := #(n U m*)


with m* = {{{m}} : k e m}

Now let's try this for say, n = 0 and m = 1. Then m* = { {{0}} }. Hence n U m* = { {{0}} } and hence n + m = #(n U m*) = #({ {{0}} }) = { {} } = 1, since { {} } ~ { {{0}} } (both sets just contain one element). Hence 0 + 1 = 1.

We use m* (instead of m) here to ensure that the number of elements in n U m* will not be smaller that the number of elements in n plus the number of elements in m.

The definition

(*) n + m := #(n U m)

just wouldn't deliver what we want. (For example in this case we would get 1 + 1 = 1.)



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