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Mathematics · Glossary

What is Sets of numbers?

Also known as: natural number · integer · rational number · real number

Definition 1.1 High School Mathematics · Chapter 1 — Numbers and Sets of Numbers
  • N\N is the set of natural numbers: 0,1,2,3,…0, 1, 2, 3, \dots
  • Z\Z is the set of integers: …,−2,−1,0,1,2,…\dots, -2, -1, 0, 1, 2, \dots
  • Q\Q is the set of rational numbers: all quotients pq\frac{p}{q} with p∈Zp \in \Z, q∈Nq \in \N and q≠0q \neq 0.
  • R\R is the set of real numbers: all the numbers that can be placed on the number line.

Examples

Example 1.3

Let us place a few numbers in the smallest family that contains them.

  • 284=7\frac{28}{4} = 7, so 284∈N\frac{28}{4} \in \N even though it is written as a fraction: always simplify first.
  • −3.5=−3510=−72-3.5 = -\frac{35}{10} = -\frac72 is rational but not an integer.
  • 0.333…0.333\dots (the digit 33 repeating forever) equals 13\frac13, a rational number.
  • 2\sqrt 2 and π\pi are real but not rational, as we are about to see for 2\sqrt 2; such numbers are called irrational.
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