Re: how

On 4/8/24 9:44 AM, WM wrote:

Le 07/04/2024 à 19:56, Richard Damon a écrit :

On 4/7/24 9:23 AM, WM wrote:

 

So, With infinite sets, a proper subset CAN be the same size as its parent.

>
Impossible.

>
Nope, PROVEN.

 Proven impossble with my matrix,

Nope, since you matrix doesn't follow the required form.
All you have done is proven that YOUR logic can yield different contractory results depending on which valid path you follow.
That means that YOUR logic system is proven INCONSISTENT, and thus BLOWN UP.

>
Since the DEFINITION of "Same Size" is the ability to make a 1-to-1 mapping between the sets.
>
Do you want to claim that two sets that you can match EVERY DISTINCT element of one to a UNIQUE DISTINCT ELEMENT of the other are NOT the same size?
>
and we can build such a mapping between the set of natural Numbers (N) with the set of even Numbers (E).

 Only handwaving by "and so on"

Nope.

 

Since for ALL elements n, a member of the Natural Numbers, there exists an element e, a member of tghe Even Nubers, such that the value of e is twice the value of n (e = 2n)
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EVERY element of N is mapped to a DISTINCT element of E.
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Try to find an exception

 In all cases there are infinitely many exceptions.
∀n ∈ ℕ_applied: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

I didn't say "N_applied", I said N.
Your problem is that YOUR logic system can't actually have N, but you still talk as if it does.
Thus, your system is BLOWN UP.
N is the FULL SET of Natural Numbers, all countable infinite number of them all the way to the unreachable (by finite operations) end.
If your logic system can't handle that, you LIE every time you mention that set.

 Regards, WM