Proof techniques

Definitions:

1. A mathematical proof of a proposition is a chain of logical deductions leading to the proposition from a base set of axioms
2. A proposition is a statement (communication) that is either true or false
3. A predicate can be understood as a “proposition” whose truth depends on the value of one or more variables.
4. Axioms are propositions that are simply accepted as truth ( doesnt need to be proved, might not be able to)
5. A proof is a sequence of logical deductions from axioms and previously proved statements that concludes with the proposition in question
6. Propositions of the form “If P, then Q” are called implications. This implication is often rephrased as “P implies Q.”

Basis proof techniques:

Direct proof

Indirect proof

Proof by cases and examples

Non-constructive proof of existence