Question

Show (prove) that the set of sequences of 0s and 1s with only
finitely many

nonzero terms should be countable.

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Answer #1

Prove for each of the following:
a. Exercise A union of finitely many or countably many countable
sets is countable. (Hint: Similar)
b. Theorem: (Cantor 1874, 1891) R is uncountable.
c. Theorem: We write |R| = c the “continuum”. Then c = |P(N)| =
2א0
d. Prove the set I of irrational number is uncountable. (Hint:
Contradiction.)

Show (prove) that the set of polynomials of degree less than or
equal to 7 with
real coefficients should be uncountable.
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Let S denote the set of all possible finite binary strings, i.e.
strings of finite length made up of only 0s and 1s, and no other
characters. E.g., 010100100001 is a finite binary string but
100ff101 is not because it contains characters other than 0, 1.
a. Give an informal proof arguing why this set should be
countable. Even though the language of your proof can be informal,
it must clearly explain the reasons why you think the set should...

Show (prove), from the original definition of the integers, that
subtraction of
integers is well defined.
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suppose that the only singularities of the function g(z) are
finitely many poles which lie away from the origin and the negative
real axis. show that integration of the function f(z)=g(z)lnz with
-pi<arg(z)<=pi , around an appropriate keyhole contour, leads
to being able to find the value of the integral g(-x)dx in terms of
the residues of f(z).

Problem 3 Countable and Uncountable Sets
(a) Show that there are uncountably infinite many real numbers
in the interval (0, 1). (Hint: Prove this by contradiction.
Specifically, (i) assume that there are countably infinite real
numbers in (0, 1) and denote them as x1, x2, x3, · · · ; (ii)
express each real number x1 between 0 and 1 in decimal expansion;
(iii) construct a number y whose digits are either 1 or 2. Can you
find a way...

(Explain each step in detail. Show your logic. Do not only
provide answers and formulas.) - PLEASE SHOW FORMULAS
You are an analyst evaluating Up-and-Coming Airlines Inc., a
very hot potential acquisition candidate your company is
considering. Up-and-Coming currently has no debt and you estimate
that it should be able to generate $1 million a year from its
existing assets (after tax cash flow). Furthermore, it has the
opportunity to invest one-half of its earnings indefinitely. You
estimate that because...

Could you please show me how to set up and calculate the
matrices for the following problem. They need to be done using
matrix multiplication. Could you please explain each of the steps
in detail because I am having trouble setting up the matrices. I
will leave feedback for you if you provide a quality answer. Thank
you.
In a toy shop there are red, blue and yellow marbles for
sale.
The toy shop sells Jumbo bags of marbles that...

show the student's calculator set-up (using the variables from a
financial calculator) and answers for each of the 3 parts in the
problem. For part c, give an exact percentage answer and not an
approximate answer. Clearly identify your answers to each part.
Assume that you just won the state lottery. your prize can be
taken either in the form of 40000 at the end of each of the next 25
years (that is 1,000,000 over 25 years) or as...

3 ONLY ANSWERS E through G, not A through D
A) Use the Lagrange Multiplier method to solve for the quantity
of X and Y when I=$1,000, Px=$25, and Py=$5, and Utility = X*Y.
Show all steps.
B) Graph budget line and utility curve. Indicate x and y
intercepts, as well as optimal bundle of x and y.
C) How many utils are obtained at the optimal choice? Show how
you obtain your answer.
D) Show the Marginal Rate of...

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