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https://math.stackexchange.com/questions/775273/contradiction-prove-22-5
math.stackexchange.com/questions/457490/22-5-error-in-proof already covers this question. –
JB King
Apr 30, 2014 at 5:26
3
By the way, it's easy to find mistakes in this sort of reasoning: just evaluate each line, one by one, and see where the expression switches from being equal to 4 to being equal to 5. –
6005
Apr 30, 2014 at 5:28
8
To summarize the answers, the point is that x2−−√≠x. Few high school students seem to realize this fact. (Ask a high school student to solve the equation x2=4 and at least half of them will say "take the square root of both sides to cancel out the square, so x=2.") What's true is that x2−−√=|x|. The equation x2−−√=x holds only when x≥0. –
symplectomorphic
Apr 30, 2014 at 5:32
BOOlean
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