We start off with quantifiers. There are two of them. “For all” and “there exists”, each with their own notation. For all is an upside down A and there exists is a backwards E. We are also introduced to predicates. a predicate is a statement that contains a variable and …

A proposition is a statement that is True or False. A large fraction of all math statements are of the if-then form. Learning about propositions, and propositions from propositions. The propositions from propositions can be combinations, modifications, or relations. For example, and, or, not. A implies B. A if and …

The Well Ordering Principle - Every nonempty set of nonnegative integers has a smallest element Proving by using the well ordering principle is another proof method. It can be used to prove that sqrt(2) is irrational. We are given the template for this proof method, along with some examples.

In this unit, we go over some proof methods. Two main ones are covered, followed by some tips about good proofs. Proof by cases Proof by contradiction I’ll spare the details here, but you can find it on the course website if you want to know the specifics. Why …

A proposition is a statement that is either true or false. We are given some examples in plain English of what is a proposition and what isn’t. Then, we go on to mathematical examples, including Fermat’s last theorem and Goldbach’s conjecture. A predicate can be understood as …