CANTOR'S POWESET PROOF <<<<EXPOSED<<<<

[Graham Cooper]

CANTOR'S POWERSET PROOF

IF SET1 has 1 - then MYSET skips 1
or
IF SET1 skips 1 - then MYSET has 1

AND

IF SET2 has 2 - then MYSET skips 2
or
IF SET2 skips 2 - then MYSET has 2

AND

IF SET3 has 3 - then MYSET skips 3
or
IF SET3 skips 3 - then MYSET has 3

AND

IF SET4 has 4 - then MYSET skips 4
or
IF SET4 skips 4 - then MYSET has 4

AND
...

SO MYSET IS DIFFERENT TO ALL THOSE SETS!

|CARDINALITY| > | INFINITY |

[Jeff Barnett]

Since this was posted in comp.ai.philosophy (but probably not relevant
there), I will respond in this group because this is the only place that
I see it. This isn't Cantor's powerset theorem or proof. The theorem is
simply that one cannot put the powerset of a set in 1-to-1 with the set
itself. You have made many mistakes here: 1) your enumeration via the
integers limits the whole idea to the denumerable, 2) there is nothing
about 1-to-1 map here, 3) Cantor's proof works for finite sets too;
infinity doesn't really come into it.

You may or may not have proved something but I'm not what sure it is.

Jeff Barnett

[Graham Cooper]

MYSET is EXACTLY Cantors missing set.

b = { n | ~n e PS_n }


Herc
--
www.BLoCKPROLOG.com

[Virgil]

In article
<6a1d75ab-3389-4a2d...@wb17g2000pbc.googlegroups.com>,

Given an arbitrary function f from |N to the powerset of |N (set of all
subsets of |N), the set S = {n in |N | ~ n in f(n)} is a subset of |N
not in the image of f, and thus is a proper "Cantor's missing set".
>
>
> Herc
> --
> www.BLoCKPROLOG.com
--