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I'm trying to prove that the following inequality holds for any $0\leq a_1,a_2,b_1,b_2\leq 1$:

$$|a_1a_2-b_1b_2|\leq |a_1-b_1|+|a_2-b_2|$$

Does anybody have an idea for proving this, or has a counter-example.

Thanks,

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Hint: $$|a_1a_2-b_1b_2|=|a_1a_2-a_2b_1+a_2b_1-b_1b_2| \leq |a_1a_2-a_2b_1|+|a_2b_1-b_1b_2|$$

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    $\begingroup$ lol, i was just writing down the same hint $\endgroup$ – breeden Jan 25 '14 at 1:03
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    $\begingroup$ Thanks! It does solve it :) $\endgroup$ – Alt Jan 25 '14 at 1:03

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