1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
telo118 [61]
3 years ago
11

Show that a subsct of countable set is countable

Mathematics
1 answer:
BigorU [14]3 years ago
5 0

Answer:

We can prove this theorem as follows:

Step-by-step explanation:

Let A\subseteq S where S is a countable set.  So we can arrange the elements of S as  a sequence S=\{x_{n}\}_{n=1}^{\infty } we have the following cases:

1. <em>A is finite</em>. If A is finite clearly it is a countable set.

2. <em>A is infinite</em>. Define the sequence of positive integers \{n_i\}_{i=1}^{\infty} as follows:

n_{1} is the less positive integer such that x_{n_{1}}\in A

n_{i} is the less positive integer grater than n_{i-1} such that x_{n_{i}}\in A..

Now, observe that the correspondence f(i)=x_{n_i},\,\,(i=1,2,3,...) is a one-to-one correspondence between the elements of A and \mathbb{N}. So, A is   a countable set.

You might be interested in
If f(x) = 4x + k and f (2) = f (1), then calculate the value<br>of K.​
andrezito [222]

Answer:

-7

Step-by-step explanation:

given f(x)=4x+k

therfore, f(2)=4*2+k

we know that f(2) =1

so, 4*2+k=1

8+k=1

k=1-8

k=-7

8 0
3 years ago
Plz help me plz f(89) = -481.4 and f(126) = -677.5
yaroslaw [1]

Answer:do u have the answer

Step-by-step explanation:

4 0
3 years ago
Ms. Hartt burns 300 calories when she runs for 1 hour. If Ms. Hartt runs 5 hours in a week how many calories would she burn?
Schach [20]
Answer: If Ms. Hartt burns 300 calories in 1 hour, and runs 5 hours in a week, she burns 1,500 calories in a week.

Explanation: 300 x 5 = 1,500
6 0
3 years ago
Somebody help me please because i’m stuck
worty [1.4K]

The question is asking for you to plug in each number in the brackets into x and solve for y, or f(x), g(x), etc. I will do no. 19 as an example:

f(x) = -3x + 1

This problem has the domains -2, -1, and 0. First, we'll start with -2:

f(x) = -3(-2) + 1

f(x) = 6 + 1

f(x) = 7

Now -1:

f(x) = -3(-1) + 1

f(x) = 3 + 1

f(x) = 4

Lastly, 0:

f(x) = -3(0) + 1

f(x) = 0 + 1

f(x) = 1

For question 23, we can use the distance formula, which is ratextime. The domain in this case is time (t). You can set up a function like this: d(t) = 60t

8 0
3 years ago
Describe a situation that could be modeled with the ratio 4:1. Your answer:
Viktor [21]
An example of the ratio 4:1 could be, in a school for every 4 girls there is 1 boy. Or something similar:)
8 0
3 years ago
Read 2 more answers
Other questions:
  • Line segment YZ was used to translate ABCDE. YZ is 6.2 inches long. What is the length of AA'+BB'+CC'+DD'+EE'?
    13·1 answer
  • How many planes can you draw through 3 collinear points?
    12·1 answer
  • Which of the following represents a valid probability distribution?
    13·2 answers
  • Will give brainlyest
    14·2 answers
  • Question 1 (1 point)
    9·1 answer
  • 3x2-5x3-x(2x2+4x) simplified
    10·1 answer
  • Simplify the fraction completly<br> 64/100
    5·2 answers
  • Solve the given equation by completing the square.
    9·1 answer
  • I Need help!!! please??​
    15·1 answer
  • Which line is being represented by the graph?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!