Real Number Definition:
A continuous quantity:
Represents a distance along a line.
Real Number Notation
We represent the set of real numbers as ℝReal 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
UncountableExtend 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 CalculatorHow does the Real Numbers Calculator work?
Free Real Numbers Calculator - 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?
What 4 concepts are covered in the Real Numbers Calculator?
- number
- 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.
- property
- an attribute, quality, or characteristic of something
- real
- real numbers
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