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GREYUIT [131]
3 years ago
10

Show by using "proof by contradiction" that the set of binary sequences {0,1}N is uncountable.

Mathematics
1 answer:
liraira [26]3 years ago
6 0

Answer:

You can prove this important result as follows:

Step-by-step explanation:

Let A be the set of all binary sequences, that is to say, \{0,1\}^{\mathbb{N}}. Suppose that A is a countable set. Then the elements of  A can be ordered as a sequence \{s_{1},s_{2}, s_{3},...\}, where each s_{i} is a binary sequence. The k\text{-th} digit of each sequence is expressed by s_{n}(k). Define the sequence s as follows:

s(k)=\begin{cases}1&\text{if}\,s_{k}(k)=0\\ 0 &\text{if}\,s_{k}(k)=1\end{cases}

Note that s differ from each s_{k} in at least one digit. Then s\neq s_n for all n\geq 1, then s\notin A. This contradicts the fact that A is the set of all binary sequences. Then A must be a uncountable set.

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Two consecutive odd number have a product of 35. What are the numbers?
Kryger [21]
5 and 7… 5x7=35
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6 0
2 years ago
1. Find the sum of the measures of the interior angles of a convex 11-gon.
OleMash [197]

Answer:

The measure of the sum of interior angles of a 11-gon is 1620^{o}.

Each interior angle is approximately 147.273^{o}.

Step-by-step explanation:

A convex polygon has the measure of each interior angles to be less than 180^{o}.

But,

sum of interior angles of polygon = (n - 2) x 180^{o}

where n is the number of sides of the polygon.

For a convex 11-gon, we have;

sum of angles of a 11-gon = (11 - 2) x 180^{o}

                                         = 9 x 180^{o}

                                         = 1620^{o}

Sum of angles of a 11-gon = 1620^{o}

To check: convex polygons' interior angles are less than 180^{o}.

so that,

each interior angle of 11-gon = \frac{1620}{11}

                                        = 147.273^{o}

3 0
3 years ago
At the beginning of a snowstorm, Evan had 3 inches of snow on his lawn. The snow then began to fall at a constant rate of 3 inch
zhannawk [14.2K]

Answer:

3+3tt=total amount of snow

Step-by-step explanation:

y=mx+b is used to show increase

In this case, b is the original 3 inches of snow. m is the constant growth, and x is tt, or the amount of time it is being compared to. y is the total.

3 0
3 years ago
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polet [3.4K]

Answer:

32π cubic units

Step-by-step explanation:

Given: r=4, h=6, v=?

Volume of cone: v=(h*πr²)/3

Substitution: v=(6*π*4²)/3

v=2*π*16

v=32π unit³ or approx. 100.530965 unit³

4 0
3 years ago
Which of the following sets of ordered pairs (x,y) is NOT a function of x?
sergiy2304 [10]

Answer:

The answer is A.

Step-by-step explanation:

hope this helps

4 0
2 years ago
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