Discrete Proof: Product of 2 irrationals is irrational?

[duragezic]

I got some fvcking Discrete crap to do and I'm having a bit of troulble trying to prove or disprove that:

The product of two irrational numbers is irrational.

Well, I think that is false, since sqrt(2) (an irrational) * sqrt(2) = 2.

But that I don't think pulling an example like that really proves it. Any ideas to get me started?

 

[DevilsAdvocate]

Dork.

 

[AbsolutDealage]

Originally posted by: duragezic
But that I don't think pulling an example like that really proves it. Any ideas to get me started?

Why would that not complete the proof? Does it give some kind of restriction on the method of the proof?

If you are simply trying to contradict an absolute statement like that, all you need is an example.

 

[klah]

The negation is logically equivalent. You can disprove a universal statement by finding an example that proves the negation, which is an existential statement.

Vx in D, Q(x)
neg: Ex in D st ~Q(x)

 

[duragezic]

Hmm, well okay I guess I'll copy the 'sqrt(2) is irrational' proof from the book then show that two irrationals product equals a rational. I thought there was some sort of systematic way, like the way they proved sqrt(2) is irrational but saying its rational (written as a/b) then finding the contradiction hence its irrational. Bah, this stuff is lame.

 

[mchammer187]

all you need is one false example to DISPROVE something

but yes you need to prove that 2 is irrational