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This seems to be a very simple question but surely because there is an infinite way of writing a=1 and b=2 in so many different forms, can you ever disprove a proof or prove something in more than one way. Thanks

jock214
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  • You can definitely prove things in many many different ways. I'm not sure what you mean by "disprove a proof," but if you mean disprove something that has been proven, then that should not be possible. We can't say it isn't possible, but if it is, all of mathematics collapses into a singularity. – Thomas Andrews Mar 27 '13 at 13:45

2 Answers2

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You cannot disprove a proof. Instead, what you are doing is proving that said proof is not a proof.

And yes, there are generally many ways to prove something. At the simplest, most things can be proven directly, by induction, or by contradiction.

Jonathan Rich
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if "disprove a proof" means "find out that a statement is false", there are many ways to do it too. The first ones I can think of are:

  • to find an explicit counterexample to the statement. If you state "there are no solution to the equation $|{3^m-2^n}|=1; m,n\ge 2$", I may say $3^2-2^3=1$.
  • to find a contradiction, that is, show that if the statement were true you would derive a result which is certainly false.
  • a variant of contradiction is to show that there cannot exist a minimum or a maximum value for a finite set; the Euclidean proof that the prime numbers are infinite works in this way.
  • still another variant is to show that a property which is necessary is not achieved. Euler showed that all nodes in the graph for a reentrant path must have an even number of edges exiting from them; the graph for Königsberg walk had four nodes with an odd number of edges, so it could not be reentrant.
mau
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