I’m leaving the river in three days. Who could voluntarily leave this campus?

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Shout Out to Finals

This finals week is a little weird for me, because I’ll have had 6 full days to study before my 1 exam on Friday, and 2 exams on Monday. I am still feeling the stress though, and when I get stressed, I start thinking about really weird things.

This week’s theme is things in my life that don’t get nearly enough praise for just existing. Here’s a list of things that’s been helping me through this odd week:

1. Rain boots.

Rain boots are so awesome. It miserable outside all of Monday and Tuesday, and I got to wear my bad-ass boots all around campus. These things are literally vehicles allowing you to walk in any kind of terrain. On my way to Kent, I walked in all sorts of mud, with no repercussions to my outfit whatsoever. 4-inch puddles? Whatever. Plus, mine specifically are super cute, and I got them at Target, so I mean, bonus points there too.

2. Schaefer’s White Board Room

photo-4I don’t know about you, but I’ve used a LOT of white boards around campus for the past two years. You wouldn’t think this, but there’s a lot of variety of quality as well. Some boards (like the one on the second floor in the very back study room) are impossible to erase all the way, and have a really weird texture. It makes you want to stop studying for the sole purpose of not having to use that weird board anymore. Others are pretty average. But this one, holy crap. I’m pretty sure it’s new or something, because it is so smooth. Which maybe wouldn’t make a huge difference, but I was only going to go through half of my micro notes today, and BAM, I did all of them. Add to that the fact that there are already markers in this room for you to use (some of them even have a ton of ink in them still!), the fact that the tables in this room are ALSO white boards (with chairs included), I don’t know why I don’t spend the majority of my time in this room.

3. M&Ms. 

Because who doesn’t love that nice pick-me-up walk over to the grind to drown yourself in your own personal comfort food. Mine just happens to be the best candy created: Dark Chocolate Mint M&Ms. Plus they’re only 95 cents. That’s 4 cents less than R Kelly’s sheets, people.

4. The free-food lady in the library.

Literally as I was writing this, a woman came around the library with candy and cookies in a laundry basket and let us pick whatever we wanted. She knows what’s up. Best librarian award goes to you, ma’am.

5. Daily Odd Compliments.

I was bored out of my mind last night at work, and I found this website with little sayings that are supposed to make someone feel better about themselves, but could also creep you out a little: dailyoddcompliment.tumblr.com. I was laughing out loud at my computer screen. It was awesome, and I would totally say any one of these to my significant other.

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6. The river. 

 Even if you’re coming back from the library at 2 AM, brain dead and ready to collapse, rest assured, passing the river will instantly calm you. I don’t think people realize that the views here are SPECTACULAR. Added bonus: sometimes you see nature in action. One time, it was around 1 AM on a random Tuesday, and I was all alone walking past the pond. I saw a heron just chilling in the pond, doing it’s thing. We had a moment.

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7. My friends. 

Yeah, it’s corny, but we’re pretty awesome. We dance when there’s not music on, laugh uncontrollably about nothing, make fun of each other to no end, eat copious amounts of food, and are completely content with laying in grass in silence for hours. So yeah, that’s fun.

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Scavenger Hunt: Done, Thank God.

Amanda and I just finished the scavenger hunt, big thanks to everyone who helped us (which was a lot of people). We’ll post all our clues later!

If anything, this scavenger hunt made me realize that I cannot do math by myself, especially under a time limit.

And that math majors are super nice and always willing to help, even if you ask them a random calc II question in the middle of the green bean.

Unrelated to anything ever

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It’s the last Thursday of classes, and I only have one class left for the semester, which thankfully is FOM. I’ll be on the other coast next semester at California State to fulfill ELAW, so I won’t be back on the river for something like 8 months.

I’m the type of person to embrace change, but dang, I will really miss the river and this campus.

Procrastination

Okay so I have this Comparative Economic Systems final in 13 days. It’s 25% of my grade, and cumulative. I basically have to know everything about capitalism, socialism, and the economic framework and history of 7 countries to the point where I could compare and contrast any aspect of them with any other country.

So instead of starting to study the insurmountable amount of information I’m required to know, or finding more clues for the scavenger hunt, I’m just going to prove that thing we talked about in class on Monday.

Using the definition of limit given, prove:

lim (x→0) x² = 0

lim(x→17) x² = 17²
The definition of limit as given before in class is: (∀ε>0)(∃δ>0) such that if 0<|x-a|<δ then |f(x) – L|<ε.
We’ll start with lim (x→0) x² = 0. First, let’s define some terms/match them up with the definition of a limit.
f(x) = 
a = 0
L = 0.
So based on the definition, if 0<|x|<δ, then |x²|<ε. Since the definition says that this definition must work for all ε>0, we just need to choose one δ that makes this statement true. If δ ≥0, this statement works, since x is approaching 0.
0<|x|<1, then |0-0|<ε, which is true because ε>0.
For lim(x→17) x² = 17²,
f(x) = 
a = 17
L = 17².
Based on the definition, if 0<|x-17|<δ then |x² – 17² |<ε.
Adding 17 to both sides, we get that if -17<x<17, then |x² – 17² |<ε, which is true, because ε must be greater than 0. No matter what you put in for x, because of the absolute values, cannot be less than 0.
That’s really all I’ve got. I thought these would be much easier to prove since we’re given a definition to plug things into, but I don’t think I proved either of these. I’m ignoring the fact that I need to assume the hypothesis is true and focus on the conclusion, and I’ve lost sight of what needs to really be proved in this statement, since we’ve got δ and ε to prove.
Dang it. And I thought I was being productive.

Clue #1

So the first clue has something to do with marbles and distributions. Amanda figured out that it has something to do with Pascal’s triangle, where Pascal’s marble run distributes the marbles in a bell shaped curve.

Also when I googled Pascal’s Marble Run this picture came up:

Is this what we’re looking for??

“Casual Thinking and Hardcore Drinking”

The above quote is one of the many reasons I love FOM/Casey. Anyways, Casey wanted us to work on proving a theorem as part of our homework this weekend, and I am 75% I figured it out last night.

Cantor-Bernstein-Schroeder Theorem: 

If ∃ injective functions f : A → B and g : B → A, then ∃ a bijection b: A → B.

Okay, so first of all we’re assuming that those two injections exist, and we’re trying to prove that those two injections mean that a bijection exists.

For f : A → to exist, there must be at least as many outputs as there are inputs so that f(a)=f(b) ⇒ a=b can be true. If there were more inputs than there were outputs, every input would not have a unique output, and would therefore not be an injection. So, based on this |A| ≥ |B|.

But, there exists another injection  g:B → A, which means that |B|≥|A| based on the same reasoning above.

For both of these functions to be injective, we need to combine |A|≥|B| and |B|≥|A|, which means that only way both injections could be true is if |A| = |B|.

For a function to be bijective in between two sets, they have to satisfy onto and one-to-one. For one-to-one, as said before, there needs to be at least as many inputs as outputs. There can be more outputs not mapped to with injectivity. But with onto, all outputs must be mapped to, so there must be at least as many inputs for all outputs. This means that for a bijection to exist, |A| must equal |B|.

Hey! We just proved that it does if there are two injections in existence!

I think this proves this, right? Word. Happy Saturday ya’ll.

Math ≠ Ambiguity (Right?)

We had a huge discussion in FOM today that brought to light some of the concerns I’ve been having with numbers lately. We talked about Euclidian Axioms, and how basically, that’s just one model that we use to reference numbers and the world around us. And get this. Basically, the type of math we use is still a working model. Some brilliant, John Nash-type could wake up tomorrow morning and find a contradiction in the math we’ve all grown to know and love.

Our best defense against it? Whenever a contradiction comes up, we go back to the axioms, and make sure there are no errors.

No offense, but that sounds a lot to me like bringing a knife to a gun fight.

This also made me think about what we’ve been proving lately in class. We went over one horse theorem in class, with a proof that proved that all horses are the same color. One subtle detail made the proof fall apart. We ended up pulling it apart because they intersected two sets – and why would you do that?!

But then I’m thinking back to another complicated set Casey showed us in class, where he did some random mathy thing (forgive me for not remembering), and said something basically to the effect of, it works, and took someone a really long time to figure out that this proof works this way, so yeah.

I see differences in these two situations obviously, but they are sort of similar to me as well. What makes math work? Does anyone really know?

I think more than ever I’m realizing that math is 20% number crunching, 5% knowing what you’re doing, and 75% acting like you know what you’re doing.

This is sort of eye-opening for me, because I’ve loved math all this time because of the lack of ambiguity.

FOM right now is just making me really philosophical. I don’t think I can handle this much longer, man.

/Completely Unrelated Blog Post/

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Since I’m a total sucker for helping people out and supporting causes, I figure I’d let everyone know that it’s One Day Without Shoes today! I bought my first pair of TOMS 4 years ago, and since then have provided 7 kids with shoes (one for one) through buying cute things, and given 1 person sight through buying a pair of their sunglasses. I know there are lots of causes out there that deserve consideration, and while I am not technically participating in ODWS this year (still rocking the apparel/shoes though!), I can tell you from past years’ experience that living without shoes for a day is extremely difficult and painful.

Imagine what it would be like if you didn’t own shoes. Or clothes. For your whole life.

I don’t know, just something to think about.

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To learn more, watch this video! It’s cool.