# Need math help with the step by step solutions for the problems below

**Question description**

Hi Borys:

Here are the problems that I need solutions for:

1) How is this solved? Identify 4 Distinct infinite sets of real numbers A, B, C, and D so that each set is contained in the next one and so that A matches B, B matches C, but does not match D. Use standard sets of numbers such as NAT or RAT etc. as choices for A, B, C, and D. Justify each conclusion.

2) Suppose that a right triangle has sides a, b, and c, which happens to be a natural (whole) numbers, with c as the largest. If only a is an even number, can it be determined whether the perimeter (a + b + c) is odd or even? How is the conclusion justified? How would the answer change if (if any) if a had been an odd nymber?

3) Show how to construct a Golden triangle whose width is 4. What is the length of this of this rectangle? What is the diagonal measurement of this rectangle? Call L/W ( length divided by width) for this rectangle G and call W/L for this rectangle g. Show that the numbers G and g satisfy G = g + 1.

4) Let D denote the set of all real numbers that can be written as a decimal point followed by some combination of the digits 3, 5, and 7. For example: .33333…, .., 77777…, 55555…, and 375375375…are among the numbers in set D. Notice that set D is contained in but not = to the interval [0,1]. Do you believe it is possible to match the set D with the set of natural numbers, i.e., NAT = {1,2,3…}? Justify the answer.

5) Divide the binary number 10,000 by the binary number 111 showing the division. Show a check for the work in binary and by converting to the decimal system.

6) Explain the “Continuum Hypothesis.”

7) Convert these repeating decimals to fractions; (a) 7.575757... (b) .959595…; and, (c) .1111111. Show how this is done.

8) Consider the capital letters of the alphabet (in
simplest form). Then determine the first three such letters which can__ not__
be “traced” (as networks). Next determine the last three which can __not__
be “traced” (as networks). Explain how the theory (Euler’s) justifies the
answers.

## Tutor Answer

## Review from our student for this Answer

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors