1. Let x, a € R. Prove that if a <a, then -a < x <a.
Please use induction to prove the following question for all
natural numbers n.
(d) Prove that vns įt<2vn.
E Transversal AB DE bisects < CDF Prove: Z3 = 26 23. Given: rs Transversal 21 is a right 2 Prove: Z2 is a right Z Exercises 23, 26
1 4.6.3. (Harder!) Let 0 < a < 1. Prove that for any n EN, (1 – a)” < 1+n·a
Prove that if |A| = |Band [B<|A|, then |A| = |B).
Prove Congruence Property 3
C3 If a=b (mod m) and c < 1, then ac = bc (mod mc)
Prove that B = {(a,b) x (c,d) | a,b,c,d EQ, a<b, c<d} is a basis for some topology on R2.
let a,b > 0 . Prove that
DI < Val
(3) 5. Suppose that f : D[0, 1] → D[0, 1] is holomorphic, prove that f'(2) < 1/(1 - 121) for all z e D[0,1].
[3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that \f'(x) < 1/(1 - 1z| for all z e D[0, 1]. [3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that f'(x) < 1/(1-1-12 for all z e D[0, 1]