Y

Y = {x||x|||P(x)|}

P(x) is the power set.



Describe Y.

Its the 25th letter of the alphabet.
It is made of two or three lines, depending on how you write it.
It comes after X and before Z.
Its equal to a number.
It can be used in many different words.

>>2

I can tell that you're from Microsoft's technical help team.

Y is the set of all sets whose number of elements is a power of two.

>>4
Nope just a fellow anon trying to help out another.

>>4
I don't think that's a set. For each set A one can form the set {A} with 1 (a power of 2) element. So Y contains a proper class and hence isn't a set.

(I'm not a set theorist so I'm not comletely sure this argument holds)

>>6
I'm pretty sure you're correct.

>>6
I didn't think about the difference between sets and classes when writing >>4, so you made a good point. I don't think you're entirely correct though (assuming ZFC):

For each set A one can form the set {A} with 1 (a power of 2) element. So Y contains a proper class and hence isn't a set.
Because of the axiom of pairing - \forall x \forall y \exist z (x \in z \land y \in z) - if A is a set, so is {A}.

Additionally, Y contains only elements on which the power set operator is defined, and the power operation is defined only on sets, so Y can never contain a proper class.

Still, you're probably correct in Y being a proper class, for other reasons.

(Note that I'm not a set theorist either)

>>8
I didn't mean that {A} isn't a set. For every set A in the class of sets you can form the set {A}. Therefore Y has a subclass in bijection (assuming this makes sense for classes in general) with the class of sets, hence Y is a proper class.

(Still sketchy arguments here.)

>>9
Ah, right; I misread you in >>6. I read "Y contains a proper class" as "Y has an element that is a proper class".

And indeed, Y is a proper class (in ZFC):
Axiom of Union: For any set F there is a set A containing every set that is a member of some member of F.
If F=Y, then A has the class of all sets as a subclass. Therefore, Y can't be a set.

Problem solved, no more sketchy arguments :)

Describe Y.

I believe you already did, OP.

What the fuck do those lines mean?

That's not any notation I've ever seen.

I assume the first one is "Such that"

Is the second, "is contained in" or something?

>>12
He meant this:
Y = { x |  |x|  |  |P(x)| }
Where the first | means "such that", the 2-3 and 5-6 pairs means "size of set" and the 4th means "divides". All are reasonably standard notation, though OP did of course omit all spacing for maximum obfuscation.

Isn't Y just the class of all finite sets?  I thought |P(x)| = |x|*|x|?

>>14
Disregard that, I suck cocks, it's 2^|x|, not |x|^2.