1. Well today I was fascinated by the divisibility proofs, and I wanted to try typing up some problems in latex. Well, that lead to a long and wild goose chase, in which I never quite found the answer to what the latex code for "does not divide" is. The current answer I'm using is, "\nmid" but it doesn't look quite the same as what I see in the book. It is the symbol that was recommended by google and detexify, though. (If you have time, could you let me know what code you'd like us to use for that symbol?)
In other news, I stared at Result 4.8 and it's connected proof for quite some time trying to figure it out. It's nice to have an example that puts so many of the things we've learned together in one example. We used the definition of evens and odds, proof by cases, ranges that aren't "the integers," and complicated vocabulary. It was a fun one. I'm am officially terrified of such a thing showing up on an exam though.
2. The world of proofs gets more interesting day by day. Today I realized just how many variables we can have in an equation and still prove it true or false. I then got to imagining the possibilities of what we could prove using lemmas. We can get some pretty complicated equations and prove them by plugging in variables for the equations themselves and lemmas and cases...the truth values of everything can be known!
The format for the congruence of integers felt really familiar to me. Then I realized that it was because it reminded me of the way that logarithms are written. I kind of doubt there's a connection, but it's probably going to help me remember it.
No comments:
Post a Comment