In a course where I have written the word “assume” more times than in the entire rest of my life, I made the mistake of an unfounded assumption today. I read the quiz question in tutorial as “prove the following statement,” when it actually said “proof.” I took that to mean that the statement was true, and I just had to prove that, tried to do so for a while, gave up, and went home. On the subway, I started running test cases in my head, and realized that the statement couldn’t be true, and that therefore I should have been trying to write a disproving proof. The counter-example that proves the statement can’t be true is when n = 7. n = 7 would make n squared 49, and 47 (49 – 2) is not divisible by any natural number. So what I learned this week is the difference between proof and prove, and to read questions carefully. Hopefully, but doubtfully, this slog entry will affect my quiz score.
Week 2
This week in CSC165, we were introduced to the concept of vacuous truth. While, initially, I found this a difficult concept to wrap my head around, it became easier to understand the more Danny repeated it (thanks, Joshua!). The basic idea of vacuous truth is that, even if the antecedent is false, the implication as a whole still stands. One suggestion i would have for Danny, when explaining this concept to new minds, would be to use real-world examples as well as the mathematical ones. There is an excellent one of these on the wikipedia page on the subject: “if I am in Massachusetts, then I am in North America.” Regardless of where the speaker of this phrase is in the world (Massachusetts or otherwise) the implication stands, even if the antecedent does not.
Big up to: http://en.wikipedia.org/wiki/Vacuous_truth (I know it’s not technically a credible source, but the information I used here was accurate)
Week 1
This being the first week of CSC165, we haven’t yet learned very much that i can comment on. I did, however, suffer through an enlightening lesson on hubris. Danny said that the streetcar problem he showed us in class hadn’t been solved since 1937, so, naturally, I spent the the next two hours trying to whittle down the possible answers through increasingly unlikely leaps of logic (from “Oh, person A is asking how old the kids are, and therefore probably hasn’t seen them in over a year, meaning that any one-year-olds are out of the question,” to “ What is the minimum age that a child could be expected to play piano?”). Finally I gave up, and 0.36 seconds later (according to google), found the answer online. Turns out that the fact that the sums were important to person B was just as important in narrowing down the answer pool as the fact that there was an eldest, two of the results have the same sum (2x2x9 and 1x6x6), and only one of those has a distinct eldest. I guess what I learned this week is that if I have to make too many assumptions, I’m probably doing it wrong.
Shout out to http://brainden.com/number-puzzles.htm
csc165 slog 