For each of the following statements, determine whether it is true or false. Giv

Question

For each of the following statements, determine whether it is true or false. Give a counterexample IF IT IS FALSE (but you do not need to prove it if it is true). A bounded above set of real numbers always has a maximum. A nonempty bounded above set of real numbers always has a supremum. A nonempty bounded above set of integers always has a supremum and a maximum. If neither the set A nor the set D is dense in X, then A union B is not dense in R. A set that is dense in X must have an infinite number of members. A set that is dense in It does NOT have a supremum. Let S = {0.001 n | n Z}. Then S is dense in R. Write out the Binomial Formula explicitly for n = 4 and n = 5. Example: For n = 2, the formula is

Explanation / Answer

a)T

b)F

c)F

d)T

e)F

f)T

g)T

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