3.4. Suppose a and b are positive integers. Prove that, if aſb, then a < b.
Let U ? Rmxn. Prove that if UTI-In, then n < m.
1. Let x, a € R. Prove that if a <a, then -a < x <a.
1 4.6.3. (Harder!) Let 0 < a < 1. Prove that for any n EN, (1 – a)” < 1+n·a
Let ne Nj. Prove that n < 2(6(n)).
Prove that if |A| = |Band [B<|A|, then |A| = |B).
Problem 3. Prove that if bn + B and B < 0, there is an N E N such that for all n > N, bn < B/2.
a < 1. Show the series on -a, a] to onverges uniformly 25.9 (a) Let 0 (b) Does the series Explain converge uniformly on (-1,1) to =0
Let A, B, C be subsets of U. Prove that If C – B=0 then AN (BUC) < ((A-C)) UB
Let X be a continuous random variable. Prove that: P(21-; < X < xạ) = 1 - a.