Show that a subsct of countable set is countable

We can prove this theorem as follows:

Step-by-step explanation:

Let where is a countable set.  So we can arrange the elements of as  a sequence we have the following cases:

1. A is finite. If A is finite clearly it is a countable set.

2. A is infinite. Define the sequence of positive integers as follows:

is the less positive integer such that

is the less positive integer grater than such that .

Now, observe that the correspondence is a one-to-one correspondence between the elements of and . So, is   a countable set.

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5

x coordinate is none

step-by-step explanation: