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.