I want to prove the following statement.

If a+2>0, then a>-2.

What does "assume by contradiction that a<=-2" mean?

  • It means this is going to be a proof by contradiction. That means assume something that's known to be false and show how that isn't right and therefore the opposite must be true.
    – Jim
    Commented Nov 26, 2019 at 4:03
  • There is a stack exchange board for math questions (at any level of expertise), which this is: math.stackexchange.com
    – Stuart F
    Commented Jan 7, 2020 at 15:55

1 Answer 1


A proof by contradiction depends on the law of the excluded middle. The law of the excluded middle, in this situation, claims that either a > -2 is true OR else a <= -2 is true.

Thus, an "assumption by contradiction" is technically a theorem in propositional logic that is not susceptible of proof or disproof.

  • 2
    You are right that this is about the Law of the Excluded Middle, but I would revise your second sentence to say: "Either a > -2 is true, or else a <= -2 is true." Given the "if ... then ..." claim in OP, it looks like their goal is to prove that, under some hypotheses, a>-2 is true. One way to show this is to assume the logical negation of that, namely that a is NOT less than -2, i.e. a >= -2. Commented Nov 26, 2019 at 15:01
  • 1
    Mathematicians who reject proof by contradiction don’t tend to get very far.
    – gnasher729
    Commented Jan 3, 2020 at 12:07
  • 1
    @gnasher729 But if they did, ... ;)
    – Phil Sweet
    Commented Jan 7, 2020 at 11:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.