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The point isn’t we need to do formal verification to test correctness. It’s that you probably wouldn’t write a program first pass and assume it is but free. So,
by jeff76 8y ago
The point isn’t we need to do formal verification to test correctness. It’s that you probably wouldn’t write a program first pass and assume it is but free. So, why would you assume beginners that don’t know how to write proofs would write correct proofs without feedback to check?
- crispyambulance 8y agoAbsolute beginners may not able to write an actual proof that their answer is correct, but at least they can verify that it satisfies the problem (depending on the actual problem). In any case, since the study of mathematics is cumulative. Even if the student can't prove or verify that their answer to a specific problem is correct they will eventually reach a point, often within the same problem-set, where inability to solve a problem will force them to encounter their gaps/misconceptions. The most important thing in a mathematics text, as with any other text, is lucidity of writing and the preparation of the student.
- jeff76 8y agoThe issue isn’t just that the person can’t write a valid proof, but that the person thinks they have a valid proof, but it is actually invalid and they don’t have feedback to know it.