Re: Two results of set geometry

MoeBlee wrote:
On Sep 28, 8:50 pm, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
MoeBlee wrote:
On Sep 28, 7:05 am, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:

It really has nothing to do with the reals or uncountability. It's about
power set, and N=S^L in general for other number bases. Sure, the power
set is always larger than the root set. I agree with that. It's obvious.
But, the reals are not a power set of the naturals, as far as I see.
No, but the set of reals bijects with the power set of the set of
naturals. So if the power set of the set of naturals is uncountable
then the set of reals is uncountable.

IF "uncountably infinite" is defined as more than "countably infintite",

'uncountably infinite' is NOT defined as 'more than countably
infinite'.

Oh. Then what makes the power set of a countably infinite set uncountable, again? It's proven to be "greater", no? Through some mechanism not unsimilar to infinite-case induction? I mean, pulllease...


like "countably infinite" is defined as "more than" finite", sure.

'countably infinite' is NOT defined as 'more than finite'.

Greater than OR EQUAL? Perhaps? Tink 'bouddit.


So, I don't know what your point is.


See? It's right here, between 0 and 1! :)

Pulllllease! I've had about enough of that. Really, it's a waste of
time....

However you think of your time does not affect that the set of real
numbers bijects with the power set of the set of natural numbers which
does not biject with the set of natural numbers.

MoeBlee




Or even, flyject!

Peace, Tony
.

Relevant Pages

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