I realize that this is a quite simple proof. I can reason the answer but cannot prove it.

problem Statement:

Say c is a real number and has the property Q if x <= y whenever x, y in real numbers with cx <= cy. Which real numbers have property Q?

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- June 7th 2009, 07:22 AMpberardihow to prove?
I realize that this is a quite simple proof. I can reason the answer but cannot prove it.

problem Statement:

Say c is a real number and has the property Q if x <= y whenever x, y in real numbers with cx <= cy. Which real numbers have property Q? - June 7th 2009, 07:41 AMPlato
- June 7th 2009, 07:49 AMpberardi
The problem statement is exactly as I have written it. Perhaps it is not a proof and that simply the answer would suffice. My other rationale is that we need to use a certain property that we know is true i.e. (x-y)^2 > 0 for x != y. If you Plato cannot formalize a proof for this then I am going to quit feeling bad about it. My only problem is that I would expect the prof to say "prove it".

- June 7th 2009, 08:04 AMPlato
- June 7th 2009, 10:41 AMGamma
Suppose , .

Case 1:

Which is property Q.

Case 2: c=0

Which is trivially property Q.

Case 3:

Which is only property Q if x=y, but Q is for all , so case 3 does not satisfy property Q.

Thus property Q is being non-negative.