Practice question · Select all that apply
Select every statement that correctly describes the role of proof in mathematics.
Hints
- Two of these describe empirical science, not mathematics.
- Recall Euler's polynomial: 40 confirmations, then failure.
Show the answer
- A. A proof proceeds from axioms, definitions and earlier theorems
- B. A proof settles a claim for all cases at once
- C. A single counterexample refutes a universal claim
Why
Proof settles all cases permanently, draws only on what is already established, and yields to a single counterexample when a claim is false. Evidence never overturns a valid proof, and no amount of case-checking substitutes for one.
Practise The Structure of Mathematical Reasoning
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