🧵 Untitled Thread
Anonymous at Thu, 21 Nov 2024 01:30:16 UTC No. 16487334
Hey I'm new to set theory. I was asked to prove:
>Prove there is a unique set A in the power set of U such that for every B in the power set of U, the intersection of A and B is equal to A.
Is my proof valid?
>Suppose A is an element of P(U). Let A = the empty set. Since the intersection of any set with the empty set is the empty set, then for every subset B that is an element of P(U), the intersection of A and B is A. Thus there exists an A in P(U) such that the intersection of A and B is A.
>Suppose A' is an element of P(U) such that the intersection of A' and B is A'. Suppose B=A, then the intersection of A' with A is simply A'. But since A is the empty set, then the intersection of A with A' is A. Thus we can conclude that A=A'. This proves uniqueness.
Correct or am I retarded?
>inb4 hurr homework question durrr
Not homework, teaching myself from a text book.
Anonymous at Thu, 21 Nov 2024 01:46:09 UTC No. 16487355
Looks gud
Anonymous at Thu, 21 Nov 2024 01:48:58 UTC No. 16487359
>>16487355
Thanks I was honestly struggling for a bit with questions like these until I realized you just kinda need to play around for a bit and figure out what works. Basically just guessing until something works out and then trying to figure out the best way to write it out in English paragraphs.
Anonymous at Thu, 21 Nov 2024 01:55:14 UTC No. 16487376
>>16487359
Pretty much. And as you solve more problems in a any area of math, you get a better intuition on which ideas work.
Anonymous at Thu, 21 Nov 2024 02:09:35 UTC No. 16487391
>>16487334
100%
If you want you can work on your clarity a bit (rather than "Suppose A..." go with "Take [math]\emptyset[/math]...", maybe begin each part with "To prove existence" and "To prove uniqueness,") but that's in preparation for a hypothetical future when you're doing this for communication rather than your own enrichment.
Anonymous at Thu, 21 Nov 2024 09:27:00 UTC No. 16487673
>>16487391
Thank you for the advice fren
Anonymous at Thu, 21 Nov 2024 09:42:40 UTC No. 16487683
>>16487334
>Suppose A is an element of P(U). Let A = the empty set.
The two contradict each other. You want either A to be an arbitrary element of P(U) or the empty set. Just skip the first sentence.
Everything else is good in the first paragraph.
>Suppose A' is an element of P(U) such that the intersection of A' and B is A'.
Didn't explain what B is.
>Suppose B=A, then the intersection of A' with A is simply A'.
A is no longer in this scope. Just use empty set instead of A, it's clearer this way.
>Suppose B=A, then the intersection of A' with A is simply A'. But since A is the empty set, then the intersection of A with A' is A. Thus we can conclude that A=A'. This proves uniqueness.
This is long and confused. I would simply say that
>If A satisfies the property, then the intersection of A with the empty set is A, but the intersection of any set with the empty set is the empty set, therefore A must be the empty set. This proves uniqueness.
Your proof is valid but you really need to work on your style and clarity.
B00T at Thu, 21 Nov 2024 10:02:29 UTC No. 16487688
>>16487683
Join your fart with mine in timed fart event.
3...
2...(Go)
1...
Go. Fart now
Anonymous at Thu, 21 Nov 2024 10:36:25 UTC No. 16487713
>>16487683
Let me guess, you're a virgin aren't you?
Anonymous at Thu, 21 Nov 2024 17:42:01 UTC No. 16488088
Idgi math hard :(