Hello all! How is everyone post-test? Did you find it easy? Personally that last question gave me a bit of trouble. "Prove floor of x > floor of x/3.0." I'm still not 100 % sure how to solve it, even with the solutions posted... Guess that's what office hours are for...
The next lesson is more implication. We already know how to solve P(n) implies Q(n). What about when Q(n) implies something else, and so does that, and so on, etc. Example: P(0) implies P(1) AND P(1) implies P(2) AND ... AND P(12) implies P(13). ........then P(0) implies P(13).
Note: "The starting point doesn't have to be zero, since the key idea is passing a property of some natural number to its successors." (Quote taken from lecture notes.)
To solve these problems though is very similar to previously learned induction; First establish the starting point property is true, then check that the property "spreads from each natural number to its successor," using "universally quantified implication."
This doesn't appear to be that difficult, but I'm sure future problems will soon prove me wrong.
Practice, practice, practice. Good luck.
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment