Journal #3

Week 4

    PROOFS!! Proofs are always my biggest enemies as I can tell if something is correct or not but not be able to explain the reason. This week I learned how to write proofs and some structures that are used when writing proofs.

For example:
"A generic proof of ∀x ∈ D, p(x) ⇒ q(x)

Assume x ∈ D                                        # x is a generic element of D
    Assume p(x)                                         # x has property p, the antecedent
        Then ...
           .
           .
           .
        Then ...
    Then p(x) ⇒ q(x)                                      #assuming antecedent leads to consequent
Then ∀x ∈ D, p(x) ⇒ q(x)                                   # only assumed x is a generic D                   "