CSC165 Lecture Week 6

This week I learned how to prove a statement about a non-boolean function, how to disprove something and how to prove a limit.

    For non-boolean functions, the most important thing for you to do is write down the definition of the function in a logical way. The definition will be used in the proof and it is much easier to use if you have a clear logical statement. To actually figure out the path to the proof, you should try to change the statement to match something in the definitions of the function.

    It seems pretty simple to disprove a statement. All you have to do is prove the negation of the statement. It is of course often easier said than done. You still have to prove some statement. To disprove a universal quantifier, the negation is an existential quantifier, so a single example is needed to disprove it. To disprove an existential quantifier, the negation is a universal quantifier, so you need to prove the negation by using some generic element of the sets in question.

   I am actually still having some trouble with limits. I've have four midterms this past week, but now that they are over I plan to spend some time practicing limit proofs and looking at some more examples. I get the basic gist of a limit statement.

If epsilon is picked first, there has to be a delta for which the implication holds true. I still am a bit confused as to how you are supposed to find a delta in relation to epsilon for which the implication is true. Once again, I'm probably just going to have to practice, practice, practice.