I have a question on something that has come up many times for me in other contexts, such as Lipschitz transforms, and recently contraction mappings and the fixed point theorem.(adsbygoogle = window.adsbygoogle || []).push({});

Is the following statement always false, and why?

Let x and y be two positive real numbers.

[itex]\exists k<1 \,\, s.t. \,\, x \leq k\cdot y \, \Leftrightarrow \, x<y[/itex]

So far, I've always seen statements like this to be false, but I'm not sure why.

Thanks,

Jesse

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# Is x<=ky equivalent to x<y?

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