Show that 1 and sqrt(2) are not commensurable.
I was given the definition "Two real numbers x and y are commensurable if there exists a real number u, and integers m and n so that m(u) = x and n(u) = y."
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I should mention this is the 3rd question. The first was a proof that any two rational numbers are commensurable.
The second was that if x, and a rational number a/b are commensurable, then x is a rational number.
I wont write both of these out but they are quite short and I used their implications for my proof. So, unless otherwise requested I will considered them assumed true.
Please post this in Mathematics group. That way there is more probability that your question will be answered.