Ok... So today, someone asked me a simple question: Why do two negatives become a positive number when multiplied together? This is intuitively basic, but not as easy to prove (unless there's some simple proof that I didn't think of). This was the basic proof that I came up with:(adsbygoogle = window.adsbygoogle || []).push({});

Let a, b, c > 0 and a, b, c [tex]\in[/tex] R.

a > 0

a/(-b) < 0/(-b)

a/(-b) < 0

a/(-b)(-c) > 0/(-b)(-c)

a/(-b)(-c) > 0

Since a/(-b)(-c) is greater than 0, and a is positive, then (-b)(-c) must also be positive. Therefore, multiplying by two negatives will produce a positive.

I know my proof isn't very good, but I am not a mathematician. I thought that I came up with a semi-decent way to show that multiplying two negatives together will produce a positive number. Now, the next question that person asked me was: Well then why does the inequality flip over when you divide by a negative? Again, it's intuitively obvious but I do not know how to prove it. Does anyone know how I could prove that or a better way to prove what I just attempted to prove?

P.S. I meant to put this in general math because it would be more appropriate there, but I accidently posted it here and cannot delete it. So maybe a moderator can move it...

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# Proving Inequalities

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