Proof by contradiction help
Hi,
I have an A Level maths proof (4 marks) and I can't see how to go about it:
Prove by contradiction that if a/b is irrational, at least one of a and b is irrational.
I get that you start by assuming a and b are both rational, but I'm not sure how to prove that would mean a/b has to be rational too.
I'd appreciate any help
I have an A Level maths proof (4 marks) and I can't see how to go about it:
Prove by contradiction that if a/b is irrational, at least one of a and b is irrational.
I get that you start by assuming a and b are both rational, but I'm not sure how to prove that would mean a/b has to be rational too.
I'd appreciate any help
Original post by e123c
Hi,
I have an A Level maths proof (4 marks) and I can't see how to go about it:
Prove by contradiction that if a/b is irrational, at least one of a and b is irrational.
I get that you start by assuming a and b are both rational, but I'm not sure how to prove that would mean a/b has to be rational too.
I'd appreciate any help
I have an A Level maths proof (4 marks) and I can't see how to go about it:
Prove by contradiction that if a/b is irrational, at least one of a and b is irrational.
I get that you start by assuming a and b are both rational, but I'm not sure how to prove that would mean a/b has to be rational too.
I'd appreciate any help
Suppose both are rational. Then both can be written as fractions. So let and be fractions in their irreducible forms, where and .
So, what is the ratio a/b in terms of p,q,r,s ?? Can you deduce that the numerator and denominator of this fraction are elements of (denominator never zero) ?? If so, that is sufficient to show that we have a rational number, which is a contradiction.
(edited 4 years ago)
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