why do we consider p and q are coprime when we are proving any irrational number
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Claim: p and q are coprime. Reason: If not, then we could just "cancel out" the common factor, and end up with another way to write the fraction with a smaller denominator; this contradicts the idea that q was as small as possible. and by Euclid's lemma you find that p is a multiple of p1.
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it is not necessary u can choose any but it impresses our work in the maths that's why it is used mostly
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