Real Number System

Classify each element of `{sqrt(7), (-1)/4, 0, 3, 1, 4, 4, 22/7}` as a member of N, Q, R − Q or Z

Prove that `sqrt(3)` is an irrational number.
(Hint: Follow the method that we have used to prove `sqrt(2)` ∉ Q)

Are there two distinct irrational numbers such that their difference is a rational number? Justify

Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number

Find a positive number smaller than `2^(1/1000)`. Justify

Choose the correct alternative:
Given that x, y and b are real numbers x < y, b > 0, then