LET US BEGIN by recalling that a variable is a symbol that takes on values.  A value is a number.

Thus, if x is a variable, then x might have the value 2, or −3, or 5.2, and so on.

 

Next, the following numbers of arithmetic are called the natural numbers:

1,  2,  3,  4,  and so on.

If we include 0, we have the whole numbers:

0,  1,  2,  3,  and so on.

And if we include their algebraic negatives, we have the integers:

0,  ±1,  ±2,  ±3,  and so on.

± ("plus or minus") is called the double sign.

These are the square numbers, or the perfect squares:

1   4   9   16   25   49   64 .  .  .

For, they are the numbers 1· 1,  2· 2,  3· 3,  4· 4,  and so on.

Rational and irrational numbers

1.  What are the rational numbers?

They are the numbers of arithmetic:  The whole numbers, fractions, mixed numbers, and decimals; together with their negative images.

2.  Which of the following numbers are rational?

 

1   −6   3½   −  2/3   0   5.8   3.1415926535897932384626433

All of them! All decimals are rational. That long one is an approximation to π.