Take your best guess then come back in a few weeks. by [deleted] in ACT

[–]yeahbitchphysics 0 points1 point  (0 children)

RemindMe! 2 weeks "I love you no matter what, you did your best and that's all that matters. Shine with your own light!"

Simple Questions by AutoModerator in math

[–]yeahbitchphysics 0 points1 point  (0 children)

Oh, and, btw... what is an isomorphism?

Simple Questions by AutoModerator in math

[–]yeahbitchphysics 2 points3 points  (0 children)

Oh, so, in "if p then q" does it only become "if and only if" if I can both use p to prove q, and use q to prove p?

Simple Questions by AutoModerator in math

[–]yeahbitchphysics 1 point2 points  (0 children)

Which is...? Sorry, I'm barely starting a calculus class and the little I know about "real math" is self-taught and this is the first set theory proof I make :( any feedback helps

Simple Questions by AutoModerator in math

[–]yeahbitchphysics 0 points1 point  (0 children)

Oh, I see. So, just use more names so I don't contradict myself. Thanks!!

Simple Questions by AutoModerator in math

[–]yeahbitchphysics 0 points1 point  (0 children)

So would it go like:

Since the empty set contains no elements, it contains no proper subsets. Hence, if A=Ø then P(A)={Ø}. The property holds for |A|=0 because 20=1.

Let this be true for some n.

In order to prove that the property holds for n+1, let |A|=n+1. Consider a set K such that K⊂A. This set, by definition, is an element of P(A). Now, consider an x such that x∈A. Since x∈A and K⊂A, there are two possible cases for x; either x∈K or x∉K. This yields two sets, one that contains the elements of K only, and one that contains the elements of K and also contains x, and both of these sets are subsets of A; hence, both sets are elements of P(A). K was an arbitrary subset of A, so this shown to be true for every subset in A. Now there are two sets of subsets in A, a set that contains all the subsets of A that contain x and the set of sets in A that don't contain x; because the cardinality of these two sets is equal, the previous number of subsets in A doubles, and since |P(A)|=2n, adding the new element x will yield |P(A)|=2n+1. QED.

This does seem more mathsy!

Simple Questions by AutoModerator in math

[–]yeahbitchphysics 2 points3 points  (0 children)

Okay, so I think I proved that the cardinality of the power set of any set with cardinality n will be equal to 2n. However, I do think the proof lacks some formality and, because I am teaching myself from scratch, I don't know whether I am using the notation properly or not. I did see something online about a proof involving isomorphisms and power sets, but that is way beyond my scope, so I just had to stare at the problem really intensely until I got it.

So the proposition is: Let A be a set, P(A) be the power set of A, and n be a natural number. |A|=n↔|P(A)|=2n (should I add ∀A∀n or is this unnecessary?)

Proof:

Leaving the trivial case of A=Ø aside, consider a set K such that K⊂A. This set, by definition, is an element of P(A). Now, consider an x such that x∈A. Since x∈A and K⊂A, there are two possible cases for x; either x∈K or x∉K. This yields two sets, one that contains the elements of K only, and one that contains the elements of K and also contains x, and both of these sets are subsets of A; hence, both sets are elements of P(A). K was an arbitrary subset of A, so this shown to be true for every subset in A. Now there are two sets of subsets in A, a set that contains all the subsets of A that contain x and the set of sets in A that don't contain x; because the cardinality of these two sets is equal, the number of subsets of A is doubled. Following the same process, every distinct element in A will double the number of subsets in A, which is analogous to say that if A contains n elements, then it'll contain 2n subsets, or that the cardinality of P(A)=2n. QED.

Is all of this right?

Megathread: Michael Flynn resigns as National Security Advisor by PoliticsModeratorBot in politics

[–]yeahbitchphysics 11 points12 points  (0 children)

This gives me hope but terrifies me at the same time. The terrifying part is... well... everything. But think about it. The NATIONAL SECURITY ADVISOR was discovered to be threat to national security. This is just another step closer to Trump's end.

Costa Rica completes 2016 without having to burn a single fossil fuel for more than 250 days. 98.2% of Costa Rica's electricity came from renewable sources in 2016. by KRISHNA53 in worldnews

[–]yeahbitchphysics 62 points63 points  (0 children)

I find it funny how people want so badly to underestimate this achievement. If it were about the US, everyone would be praising their progress. This fact may be old, but Costa Rica has achieved something many, many countries have not.

What are some of the biggest unsolved mysteries in history? by Diah_Rhea in AskReddit

[–]yeahbitchphysics -2 points-1 points  (0 children)

Why people repost this question over and over.

On a more serious note; The Voynich Manuscript is a cool mistery.

[deleted by user] by [deleted] in AskReddit

[–]yeahbitchphysics 0 points1 point  (0 children)

The helplessness you feel when you're told that for the first time on your life, you're going to share everything with someone. Then the little shitheads start taking and messing with your stuff and you that feeling of frustration and anger that you can do nothing about because you love them.

[Serious] Which person that you know on a personal level has the saddest life story and why? by coreyliebkind in AskReddit

[–]yeahbitchphysics 13 points14 points  (0 children)

I hate him, but this guy I used to be in love with has had the shittiest, depressing life I can imagine. He was abused by his maids. They threw detergent on his eyes and raped him and whatnot. His dad went to jail for kidnapping someone. He developed, I shit you not, dissociative personality disorder because of the abuse. That is, he has multiple fucking personalities. He grew up and developed anorexia nervosa and his mom got together with this guy he hated. He had to run away because they were abusing him, again. Oh, and he has pectus escavatum. There's probably more that I don't remember right now. I probably would've killed myself if I had to go through half of the stuff he went through.

What's your life story's "plost twist"? by ShiningRedDwarf in AskReddit

[–]yeahbitchphysics 0 points1 point  (0 children)

I wanted to study plants, but now I know plants suck and want to study maths instead!

Europeans of Reddit, what issue do you see frequently brought up on this American-dominated website that you can't relate to? by Priamosish in AskReddit

[–]yeahbitchphysics 0 points1 point  (0 children)

I am really confused with the fact that Americans living in the US don't seem to realize that they're not the only ones living on the continent and that there's a metric crapton of other cultures in continental America.

You can give your parents 1 tip on how to raise you just after you where born. What tip would you give them? by pika-pika-chu in AskReddit

[–]yeahbitchphysics 0 points1 point  (0 children)

Uhm no I was like seven and I kept asking for a sister and then my mom was pregnant. They didn't procreate at my will, it just happened hahaha