A Discrete Math textbook first proved that the statement:(adsbygoogle = window.adsbygoogle || []).push({});

0 < x < 1 -> x^2 < 1

is true (I have no problem following the proof).

It then went to prove the contrapositive:

x^2 >= 1 -> x <= 0 or x >= 1

Here's the proof:

Assume x^2 >= 1. (no problem here)

If x <= 0, we have the desired result, so assume x > 0. (what?!?)

The last part I wrote bedazzled me. What does the book mean when it says: "If x <= 0, we have the desired result"? For an implication to be true, the hypothesis and conclusion must be true. We already assumed that the hypothesis is true. Now for the conclusion to be either the left side of the OR statement is true or the right side is true. How can the book conclude that x <= 0 is true?

thanks a lot

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# Confusing Proof

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