(i) Prove that if r is a rational number, then r - √√2 is irrational. (ii) For any two real numbers a and b, assume that the number of elements in the interval [a, b] is larger than the number of all rational numbers. Show that between any real numbers a and b, there must exist an irrational number. (Assume there is no irrationals between a and b and get a contradiction to the assumption.)

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