Week 6- Further Proofs

Furthering our discussion on proofs, we learned some more structures for proofs this lecture- more complex ones, involving more thinking.

First of all, we focused on non-boolean functions. Quantifiers cannot be applied on functions, so in order to prove a function we need to be creative. Using the definition of the functions, we can define many inequalities and comparisons that we may find useful when proving a statement. The takeaway is to manipulate expressions into forms closer to those in the definition.

Next, we learned to disprove statement by finding one counter-example- similar to what we have done before. We negate  the statement, then draw examples to find a counter-example.

Lastly, we tackled limits. This is a tricky one as this involves thinking backwards to find a proof. The example in class was tough to understand, but once I read it over again the method for finding a correct delta- the hard part is finding the start point.