Real Numbers

Real Number Definition:

A real number is a value of a continuous quantity that can represent a distance along a line.

Real Number Notation

We represent the set of real numbers as ℝ
Real numbers extend from but do not include (-∞, ∞)

What do Real Numbers Include?

Natural (Counting) Numbers (ℕ) (1, 2, 3, 4, ...)
Whole Numbers (0, 1, 2, 3, 4, ...)
Integers (ℤ) (..., -3, -2, -1, 0, 1, 2, 3, ...)
Rational Numbers (ℚ) (1/2, 0.8, 3.5, ... )
Irrational Numbers (like π, Euler's Number (e) = 2.718281828459, √2, etc)

What do Real Numbers NOT Include?

Positive Infinity ∞
Negative Infinity -∞
Imaginary Numbers like i = √-1

Properties of Real Numbers

Extend infinitely (but do not include infinity)
Any non-zero real number is either negative or positive.
Real Numbers can be ordered
The sum of two non-negative real numbers is a non-negative real number: x ∈ ℝ, y ∈ ℝ → x + y ∈ ℝ
The product of two non-negative real numbers is a non-negative real number: x ∈ ℝ, y ∈ ℝ → xy ∈ ℝ

Properties of Real Numbers:

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Real Numbers Calculator:

To see if a number is real, you can ask the search engine questions like is 15 a real number

How does the Real Numbers Calculator work?

This lesson walks you through what real numbers are, how to write real numbers, real numbers notation, and what‘s included in real numbers

What 2 formulas are used for the Real Numbers Calculator?

  1. ℝ → (-∞, ∞)
  2. Represents a distance along a line

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Real Numbers Calculator?

an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.
an attribute, quality, or characteristic of something
real numbers

Real Numbers Calculator Video


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