]> Exercise 1.1

Exercise 1.1

Is countable?

Solution:

Though there are "twice as many" positive and negative integers as there are only positive ones, we can make a one-to-one correspondence between and . We can, in other words, assign a unique positive integer to each positive and negative integer.

How? Assign the positive integer 2 n + 1 to the positive integer n , and the integer 2 n to the negative integer n . The correspondence looks like this:

:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

...

:

0

-1

1

-2

2

-3

3

-4

4

-5

5

-6

6

-7

7

-8

...

Sooner or later you get to every element of this way, though the elements of grow faster than those of . The peculiar fact, but fact nevertheless is that it doesn't matter at all that the elements of grow faster here.