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


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.)

