1. Find the supremum and infimum of the following sets. (c) { (a) {, e} (b)...
5. Describe the following sets of real numbers and find the supremum and infimum of these sets: (a) {x}\x2 – 2 <4€R} (b) {x|x+ 2 +13 – x4<4} (©) {x|x<for all neN} 6. For any two elements x and y of an ordered field, prove that _x+ y + x- x + y - x - y (a) max{x,y}=- (b) min{x,y}=-
7. Find the interior and boundary of each of the sets(VR:nEN) and r EQ:0<< 2
[3] 5. Suppose that f: D[0,1] for all z E D[0, 1] D[0,1] is holomorphic, prove that \f'(z) < 1/(1 - 121)2
A) B) C) 1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
2, For each of these sets. A={3n : n E N), B = {r E R : x2 < 7), and C = {x E R : x < 12), (i) Is the set bounded above? Prove your answer.] ( .] ii) Is the set bounded below? Prove your answer answer the following questions:
2. Define the relationships (C, C,), if any, among the following sets: A={x : 0 < x < 1} B={x : 0 < x < 1} C={x : 0 < x < 1} D={x : 0 < x2 <1} E={x : 0 S1 < 1 / 2 and 1/2S1 1}
Let S function, f: S R, between the two sets. x < 1}. Show that S and R have the same cardinality by constructing a bijective x E R 0
real analysis questions Find the interior of the following sets. (1): {1/n: neN}: (2): (0,5) (5, 7); (3): {re Q:0<r <2}. Classify each of the following sets as open, closed, or neither. (1): {: | - 51 < 1}; (2): {x: (x-3) > 1}; (3): {:13 -4)<4}.
all three questions please. thank you Prove that for all n N, O <In < 1. Prove by induction that for all n EN, ER EQ. Prove that in} is convergent and find its limit l. The goal of this exercise is to prove that [0, 1] nQ is not closed. Let In} be a recursive sequence defined by In+1 = -) for n > 1, and x = 1. Prove that for all ne N, 0 <In < 1....
Provided N(0, 1) and without using the LSND program, find P( - 2 <3 <0) Provided N(0, 1) and without using the LSND program, find P(Z < 2). Provided N(0, 1) and without using the LSND program, find P(Z <OOR Z > 2). Message instructor about this question Provided N(0, 1) and without using the LSND program, find P(-1<2<3). 0.84 Message instructor about this question