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Let {x1, x2, x3, x4, x5} be distinct real numbers. Prove there are indices a, b with 0< xa-xb<1+xaxb.

Seriously I have no idea how to even start...

I tried subbing random numbers in... but nope...

Can anyone give a hint?

Hey wait, the sets do not need to be ordered right? Can I do this?

Direct proof:

{x1, x2, x3, x4, x5} = {-1, -2, -3, -4, -5}

proven.

Seriously I have no idea how to even start...

I tried subbing random numbers in... but nope...

Can anyone give a hint?

Hey wait, the sets do not need to be ordered right? Can I do this?

Direct proof:

{x1, x2, x3, x4, x5} = {-1, -2, -3, -4, -5}

proven.

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