Consider the following “proof”. 3 > 2 3 log 0.5 > 2 log 0.5 log(0.5^3 ) > log(0.5^2 ) 0.5^3 > 0.5^2 0.125 > 0.25 Clearly this is wrong! We started with a true statement 3 > 2, performed some algebra, and arrived at an incorrect statement 0.125 > 0.25. Which step(s) are correct? Why? At which step(s) did we make a mistake? Why?

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