# 数学Assignment代写：Mathematical Analysis MATH3611，85+ Pass

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## 数学Assignment代写案例：MATH3611 Higher Analysis

1.Let A be any infinite set and B any countable set. Prove that |A| = |A ∪ B|. That is, prove that there is a bijection from A to A ∪ B.

2.A 2-D lattice walk is a (finite or infinite) list of points in Z 2 , starting at (0, 0), and with each subsequent point distance 1 from the previous point. For example (0, 0),(1, 0),(1, 1),(1, 2),(1, 1) is a 4 step lattice walk. Are the following sets countable or uncountable?

(a) The set Wf of all finite length lattice walks.

(b) The set W of all infinite length lattice walks.

(c) The set W42 of all infinite length lattice walks which are never more than distance 42 from the origin.

3. Let X = R 3 , and define, for x = (x1, x2, x3), y = (y1, y2, y3) ∈ X

d(x.y) = max i=j |xi − yi | + |xj − yj |.

Determine whether d is a metric on X. Prove your answer. (For amusement: what does the set {x ∈ R 3 : d(x, 0) = 1} look like? How many faces does it have?)

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