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### Help with a Proof

```
Date: 6 Apr 1995 14:27:55 -0400
From: Loic Dachary
Subject: Proof

I'm trying to figure out how to prove that a is less than b
implies that a * a is less than b * b  is true in R+

I'm not having any troubles with a is less than b, then a * a is
less than b * b, but the opposite is beyond my capabilities.

Can you help ? Thanks in advance,
Loic
```

```
Date: 7 Apr 1995 10:58:03 -0400
From: Dr. Sydney
Subject: Re: Proof

Hello, Loic!

Now, I'm not sure how rigorous you want to be with this, so if you want more
rigor, just write back, and we'll be happy to help out.

Let's assume that neither a nor b is 0 (you can address the case where a
is 0 in a special case....write back if you aren't sure how to do that).
Then, we can divide both sides by a*a right?  (If you want a rigorous proof
of this, let us know!)  So, then you have the inequality :

1 is less than (b/a)^2

How does this help?  Try and work with this, and see if you can come up with
a proof!  If this doesn't seem to be going anywhere and you want a little
more help, or you want to try a different tack on the problem, just write us
back!

--Sydney, "dr. Math"
```
Associated Topics:
High School Basic Algebra

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