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The proof of this theorem requires the Archimedean Property and when we apply this property, we let $a$=_________ and $b$=________

I do not understand what $a$ and $b$ equal. Can someone please explain this property to me?

Akamazinggg
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  • Hi @Akamazinggg, try to make the statemented clear, I do not understand what you are asking. Maybe you can also have a look here, it seems related (and probably it is the answer to your question): https://math.stackexchange.com/q/189086/532409 – Quillo May 08 '20 at 08:34

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I am not sure what $a$ and $b$ are meant to be, but the idea behind the proof is that if we have two distinct real numbers $x$ and $y$ then $|x-y| > 0$, so the Archimedean property of the rationals tell us that we can find a rational number $\frac 1 q$ such that $\frac 1 q < |x-y|$. Can you see how this helps you find a rational number that is between $x$ and $y$ ?

gandalf61
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