Proof

proof by induction

• variable
• property
• base case
• induction hypothesis
• induction step

direct proof

contrapositive proof

$P$ implies $Q$ is equivalent to $\sim Q$ implies $\sim P$

proof by contradiction

assume $\sim P$ is true, get a contradiction

circular proof

to prove $(1)\iff (2)\iff (3)$, need only prove $(1)\Rightarrow (2)\Rightarrow (3)\Rightarrow (1)$

Last edited: 2024-09-13