Practice question · Fill in the blanks
Complete the summary of this unit.
A universal claim is refuted by ______, but established only by a general argument.
Word bank: many examples · one counterexample · one example · a definition
Hints
- Recall the asymmetry that runs through the whole unit.
- Refutation is cheap; proof is not.
Show the answer
A universal claim is refuted by one counterexample, but established only by a general argument.
Why
One counterexample refutes; only a general argument proves. This asymmetry — cheap refutation, expensive proof — is the single most important idea in the unit, and it is why mathematics rests on proof rather than on evidence.
Practise The Structure of Mathematical Reasoning
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