Quantifiers
Introduce universally quantified variables, apply universal hypotheses to specific values, give witnesses for existence claims, and extract witnesses from existential hypotheses. The course ends with a mixed review without step-by-step guidance.
Progress is kept in this browser until you sign in
- Prove a statement about every numberintro n picks an arbitrary n. Whatever you prove holds for all of them.15 min
- Use a universal hypothesisA ∀-hypothesis is a function: apply it to the value you need.13 min
- Provide a witnessTo prove ∃ n, …, name the n and prove the property for it.14 min
- Use an existential hypothesisobtain ⟨n, hn⟩ := h gives you the witness and its property.16 min
- Specialize a hypothesisNarrow a general fact to the one instance your goal needs.14 min
- Combine both quantifiersBuild an existence proof whose witness comes from a hypothesis.17 min
- Review: four quantifier movesIntroduce, apply, witness and open quantifiers in mixed exercises, with no step checklist.18 min