Proofs
You've seen how we can use mathematical notation to represent logical arguments. Now, we'll turn our focus to specific kinds of arguments: proofs.
Outside of math, 'proof' means evidence, a trail of footprints that indicates the truth. In math, a proof is a kind of argument that convinces us about the truth of a mathematical statement. Because math lets us be precise about the way our terms are defined, we can be certain about mathematical proofs in ways we can't ever be quite certain about 'proof' in the rest of our lives.
These lessons will focus on some typical patterns for proving statements, and introduce the quantifier notation for forming statements that apply all of the time or some of the time.
Topics
- Quantifiers
- Proof by contradiction
- Direct proofs
- Indirect proofs
- Proof by contrapositive