A place for sharing things

I know people are curious sometimes about how much time they've spent reading and stuff and turns out you can actually find out sort of! Check it! It also shows everyone elses stats but whatever. At least it gives you an idea of how far along you are and what else you need to do to get to the next level!

shill2

OMG Qurat you are so awesome! This is so helpful! Thank You!

jmacdona

http://www.maa.org/news/on-this-day

This day in math news

348 years ago today Newton became a fellow at Trinity College, London. Seems appropriate considering he's a founder of calculus.

Cromer

Ever read a book on a proof-based math subject with some truly awfully explained theorems (our textbook is not a particularly good example of this; Abbott did pretty well) that made you cringe? Want to recreate the experience for fun? Well, Theorem of the Day generator at http://davidsd.org/theorem/ has you covered!

In all seriousness, some of them can be pretty funny.

caiken1

Great find Cromer... Thanks for sharing!!!

sfrye

So, in searching for examples to work similar to homework 4, I found this handy little list of techniques for open and closed sets:

To prove that a set is not open, one can use one of the following:
Find one of its point which is not an interior point.
Prove that its complement is not closed.

To prove that a set is closed, one can use one of the following:
Prove that its complement is open.
Prove that it can be written as the union of a finite family of closed sets or as the intersection of a family of closed sets.
Prove that it is equal to its closure.

To prove that a set is not closed, one can use one of the following:
Prove that its complement is not open.
Prove that it is not equal to its closure.

This may not help proving that the reals and empty set are the ONLY "clopen" sets but it will help us prove that R and $\emptyset$ are both open and closed.

jmacdona

@sfrye It's pretty easy to see that in any Topological Space the $\emptyset$ is both closed and open. Since Our Toplogical Space is $\mathbb{R}$ in this case the compliment of the empty set is $\mathbb{R}$ itself. Since $\emptyset$ is closed, $\mathbb{R}$ is open; and since $\emptyset$ is open we see that $\mathbb{R}$ is closed. So, $\mathbb{R}$ is both open and closed.

rlewis1

Thanks, Gaither! I think this will be helpful, and not just for the homework problem.

ediazloa

Qurat is awesome!!!!!!!!

Cromer

I really think we should stop focusing so much on the analysis and focus more on the REAL part of class. For instance:
I really enjoy the taste of old garbage.
How's that for REAL.
Analyze that!

Edit:
I will share a piece of advice - don't trust anyone who's name starts with G and ends with aither with your unlocked computer.

sfrye

I concur! That is an excellent motto to live by.

gbrock

You're kinda awesome.

But I wouldn't say that outside of the internet.

TheBearMinimum

Thanks to this post I find it necessary to share the Hitler Learning Topology video. Thanks, rlewis.

rlewis1

I can't take all the credit. @Spiff showed me this.

caiken1

Hey Cromer, want to grab some garbage tomorrow after class? I would like to discuss some of the in class problems over some fresh steaming rotten banana peels on Styrofoam. I also know a great place to get gnocchi that's straight out of Italy('s garbage).

caiken1

Thanks to whomever typed this onto my account while I was away from my computer, I needed another reply. I just wished that it had been in another topic.

violincounter

shill2

And after the test...

Special thanks to @violincounter and @jmincey for the help uploading