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 durrrNot homework, teaching myself from a text book.
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>>16487355Thanks 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.
>>16487359Pretty much. And as you solve more problems in a any area of math, you get a better intuition on which ideas work.
>>16487334100%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.
>>16487391Thank you for the advice fren
>>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.
>>16487683Join your fart with mine in timed fart event.3...2...(Go)1...Go. Fart now
>>16487683Let me guess, you're a virgin aren't you?
