3.1 Natural numbers
While there are special and famous numbers like π, the numbers we use for counting are much simpler: 1, 2, 3, …. I might say ‘‘Look, there is 1 puppy, 2 kittens, 3 cars, and 4 apples.’’ If you give me 2 more apples, I will have 6. If I give my sister 1 of them, I will have 5. If I buy 2 more bags of 5 apples, I will have 15 in total, which is 3 × 5.’’ The set of natural numbers is the collection of increasing values
{1, 2, 3, 4, 5, 6, 7, …}
where we get from one number to the next by adding 1. 0 is not included. The braces ‘‘{‘‘ and ‘‘}’’ indicate we are talking about the entire set of these numbers.
When we want to refer to some arbitrary natural number but not any one specifically, we use a variable name like n and m.
The set of natural numbers is infinite. Suppose otherwise and that some specific number n...
