(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given any 2 reals a<b there exists an irrational number t such that

a<t<b . It tells us to use a theorem that states there is a rational number between any 2 reals.

3. The attempt at a solution

so If we use this and pick reals of the form p=a-√2 and q=b-√2

so now we have a-√2<t<b-√2 , and t is a rational number. then we add √2

to everything so we get a<t+√2<b

so now t+√2 is irrational , so now we have an irrational between any 2 reals.

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# Proof about irrationals between reals.

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