Question

Prove or disprove: There exist rational numbers a and b such that a^b is irrational. What kind of proof did you give?

Answer 1

For there exist proof you just come up with in a and b such that we you are trying to show is true!

for example,
Prove there exist integers m and n such that m+n=5
Proof: Set m=1 and n=4. Then m+n=1+4=5.\\
Proof done.


Do you know what rationals are?

Answer 2

oh this was 2 days ago
probably not around anymore :p

Answer 3

just "there exists", not all, hence arbitrary pick an irrational number, let say \(\sqrt 5\)
then set a = 5, b = 1/2, hence \(a^b = \sqrt 5\) irrational!!