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1. Give a counter example and then prove why, i.e., a metric space and a sequence, that disproves the claim: Every Cauchy sequence converges.
2. On the other hand, give an example of a metric space and then prove why in which every Cauchy sequence converges.
Let G be an undirected graph, and let T be the spanning tree genereted by a depth-first search of G. Prove that an edge of G that has no corresponding edge in T cannot join nodes in differect branches of the tree
Let f be a function f . Z → Z x Z such that f(n) = (2n, n + 3). Verify whether this function is 1-1 and whether it is onto and let f be a function f . R3 → R such that f(x, y, z) = xyz. Verify whether this function is 1-1 and whether it is onto.
You are driving to Columbia, SC and due to a traffic jam can only go 30 Mph for the first 20 miles. After that you drive the remaining 90 miles at 60 mph. Sketch a graph of distance versus time and one of speed versus time.
The U.S. Postal Service reports that we open and read 78% of the junk mail that we receive. A sports instructional video tape company sends out 10, 500 advertising brochures. How many of the brochures can it expect to be opened and read?
Two trains leave stations 266 miles apart at the same time and travel toward each other. One train travels at 90 miles per hour while the other travels at 100 miles per hour How long will it take for the two trains to meet?
Population growth rate
if five angles of a heptagon have measures of 80, 85, 175,90,and140 and if the other two angles are congruent what is the measure of each of the other two angles.
consider an election with 1025 voters. Suppose that at least 129 votes are needed to have the plurality of the votes. What is the number of candidates in the election?
If I am correct, the answer guide says this one converges but my answer is going to infinity which is diverges. I need to see your steps to compare with mine please.
Suppose that E is a normed linear space, and C is a subset. Prove that C is weakly bounded if and only if C is norm bounded. Conclude that weakly convergent sequences in E are bounded.
The ages of the members of a gym have a mean of 47 years and a standard deviation of 10 years. What can you conclude from Chebyshev's theorem about the percentage of gym
Write a simple program to display a fibonacci number with rule as example
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