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/sci/ - Science & Math


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11631865 No.11631865 [Reply] [Original]

Does CH imply the existence of infinite sets?

>> No.11632178

No, that guy in the other thread was just being a faggot.
CH is nonsense if you don't accept Cantor's diagonalization "argument" (and you shouldn't, it's shit).

>> No.11632219

>>11632178
>Cantor's diagonalization "argument" (and you shouldn't, it's shit).
Which diagonalization argument are you referring to exactly? Why do you think it's shit?

>> No.11632281

>>11632219
nvm, changed my mind, it's genius

>> No.11632294

>>11632281
?

>> No.11632602

>>11632281
asspained infinitard detected
enjoy your mental illness creating infinities of infinities in your head

>> No.11632626

>>11632178
anyone who thinks this hasn't seen the generalized argument. it's insanely clever. easily one of the best arguments ever discovered that has been used in many big problems.

>> No.11632685

>>11632626
>anyone who thinks this hasn't seen the generalized argument.
Sorry buddy I have, it's shit. It relies on actualizing infinity.
>easily one of the best arguments ever discovered
You need to read more.

>> No.11632694

>>11632685
>Sorry buddy I have, it's shit
Surely you're able to reproduce the argument then? Point out the part where it "relies on actualizing infinity".

>> No.11632743

>>11632694
>Point out the part where it "relies on actualizing infinity".
Precisely when it takes a power set of a countably infinite set. Are you new to this?

>> No.11632838

>>11632743
>are you new to this
Yeah, you're the first person I've talked to who thinks the argument is shit.
I don't agree with you. First of all, it doesn't take the power set of a countably infinite set. The mere statement of the theorem is
"for all x, y, if y is the power set of x then there cannot exist a bijection f between x and y". Do you think the statement I just wrote is true and is Cantor's argument a valid proof of it? Surely believing the statement doesn't require you to actually believe that you can take the power set of any set. "x is a power set of y" merely means that
[math]\forall z [z \in x \iff \forall w (w\in z \implies w \in y][/math]

>> No.11632847

>>11632178
t. retard

>> No.11632852
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11632852

>>11632602

>> No.11633281

>>11632838
>Surely believing the statement doesn't require you to actually believe that you can take the power set of any set.
Oh, so you are a retard. That's OK, I'll walk you through this.
Cantor's theorem is that this holds for *any* set. So what happens in the case that x is a countably infinite set?
Of course, you would miss cases, because you've clearly never seriously reasoned before about anything that you believe.
Cantor's theorem doesn't work unless you actualize infinity. Give up.
>>11632847
>t. butthurt baby w/ no argument

>> No.11633347

>>11633281
Anon... you disappoint me. You didn't even say if you agree or not with my statement of Cantor's theorem.

>> No.11635086

>>11633347
You're impossibly retarded and it was demonstrated quite clearly why you were wrong. You're only still posting out of impotent asspain.