1+1=2

OFFICIAL NOTICE: Until otherwise notified, please assume that this blog IS devoted entirely to math. Because I apparently never have anything interesting to say about anything else.

More about the introductory proof-writing class. We've spent the last couple days proving things that, up until this point, we simply accepted as true. Like this: If a>b, then a+c>b+c. Meaning you can add something to both sides of an inequality and the inequality is still true (for example: since 2>1, 2+3>1+3.) Obvious, right? Most of us probably used this kind of thing back in middle school, if not earlier. But actually writing a formal proof is not quite the same thing. Of course we can all SEE that the statement is true, but why it's true (and the steps to get there) are more important. It requires a different style of thinking than other math we've done up to this point, although once you get the idea it's actually kinda fun. So anyway, after a few days of proving stuff we always thought we knew, our professor writes this on the board:

1+1=2

And asks, "Why?"


You have never heard a more silent room.


Please note, this is a room full of math majors.



Thinking about it still makes me giggle.


After about 10 seconds, people started throwing out ideas, none of which were particularly correct. But at least we were trying.

It turns out it's true by definition. 2 is defined to be the sum of 1 and 1. Which was awfully nice, because none of the assumptions or theorems we had to work with were getting us anywhere close.

I love this class.

I lied.

Although I said every post in this blog wasn't going to be about math, I'm three for three here. I may have doomed myself from the beginning with the title. Stick with me, and I'll try to have something else on my mind someday.

I'm taking Transition to Abstract Mathematics, which is neither as frightening nor as impressive as it may sound. It's about writing proofs, and before we get to actual proof writing (which I should be working on now, but that's beside the point), we've learned some basic logic. Lots of if-then statements, with some ands, ors, existential and universal quantifiers thrown in for good measure. We've been playing around with these a lot in preparation for some simple proofs.

The point: As I left class on Friday (my last class, the last day of the week), I realized I was pretty tired, and though it might be a good idea to get something caffineated for my (hour-and-then-some) drive home. The thought that popped into my head?

"If it's hot in my car, then I'll go to Starbucks and get an iced Chai tea latte."

I then proved to myself I've been spending too much time in that class.

This is logically equivalent to "Either NOT the first thing, or the second thing". Meaning, either it's not hot on my car, or I go to Starbucks and get an iced Chai tea latte.

Converse: "If I go to Starbucks and get an iced Chai, then it is hot in my car." (Not logically equivalent to the first statement... I could go to Starbucks for an iced chai even if my car was a cooler temperature.)

Inverse: "If it's not hot in my car, then I won't go to Starbucks and get an iced Chai."
(Also not logically equivalent to the first, for the same reasons above.)

Contrapositive: "I don't go to Starbucks and get an iced Chai, so it isn't hot in my car." (A-ha. This one IS logically equivalent!)

All this nonsense occured to me on the walk from my class to my car, at which point I decided that this train of thought was evidence that was certainly in need of both an iced Chai (veinte, in case you were wondering) and a relaxing weekend. After both, I think I'm ready to go tackle my homework. Because: IF I don't do the homework, THEN I won't understand what's going on in class tomorrow.