The counting numbers {1, 2, 3, 4, 5, ...} are countable.
Any set that can be arranged in a one-to-one relationship with the counting numbers is also countable.
For example we can show that integers {..., -3, -2, -1, 0, 1, 2, 3, ...} are countable following this method:
• 0 -> 1
• 1 -> 2
• -1 -> 3
• 2 -> 4
• -2 -> 5
• 3 -> 6
• -3 -> 7
• etc
Note that the list has all integers on the left, and all counting numbers on the right.
We can use a similar method to show that even numbers are countable, as are odd numbers, and many other sets too.
BUT real numbers and a lot of other sets are not countable!