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.

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation:

final total: 63

step-by-step explanation:

60 times sales tax

60 times 0.05

3

60 + 3

63