Suppose you want to prove statement A. To do this, you assume another statement, B, to be true. Using statement B, you prove A. Then using A, you prove B. Would this be a valid way of proving A? If not, what are some counter-examples?
Are circular proofs valid
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proof-writing
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0Well, if you assume that 0=1 (statement B), then you can prove that 0=2 (statement A), and using this you can prove that 0=1. However all of that is nonsense. – 2017-02-14
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0In its purest form, this is called _assuming what was to be proved_, or [_begging the question_](https://en.wikipedia.org/wiki/Begging_the_question). No, it is not a valid proof technique of $A$ (though if the reasoning is otherwise correct, it shows "$A$ if and only if $B$"). – 2017-02-14
3 Answers
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I wish to prove that apples and oranges are the same.
I will assume all apples and oranges are the same. This implies the first statement. That statement implies this statement.
I hope this will suffice.
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Statement $A$: $1<0$
Statement $B$: $0>1$.
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You can try to prove A:=$2>5$, assuming B:=$ 3>6$. Assuming B you can easily prove A subtracting one at both sides. Clearly A is false