Irrationality Proof : Prove that log(8) / log(9) is irrational.
Prove that log(8) / log(9) is irrational.
Irrationality is proven. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
Proof of the Irrationality - 2. Apply the proof of the irrationality of sqrt(2) to a) sqrt(3) and b)
sqrt(4). If the proof breaks down, indicate precisely why.
3. Euler's phi-function is defined such that for n > 0, phi(n) ...
Irrationality of Pi-Squared and Repeating Decimals - 1. Show that (pi)^2 is irrational (I mean pi to the 2nd)
2. Write 12.999 as a fraction.
3. Explain why the ratio of 2 integers must always be a repeating decimal?
4. Suppose that you have ...
Algebraic Number Theory - Problem 1: Prove that there are no integers x, y, and z such that
x^2 +y^2 + z^2 = 999
Problem 2: Show that square root of 2 cubed is an irrational number.
Problem 3: F ...