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A real number is a value that represents a quantity along a continuous number line. Real numbers can be ordered. The symbol for the set of real numbers is , which is the letter R in the typeface "blackboard bold".
The real numbers include: counting (natural) numbers (),
whole numbers , integers () <. , -3, -2, -1, 0, 1, 2, 3, . >,
rational numbers () (such as -½, 6.25, ) and
irrational numbers (such as ).
FYI: The series of three dots ( . ), seen within the sets above, is called an ellipsis .
As used in mathematics, the ellipsis means "and so forth".
The properties of the Real Number System will prove useful when working with equations, functions and formulas in Algebra, as they allow for the creation of equivalent expressions which will often aid in solving problems. In addition, they can be used to help explain or justify solutions.
Don't panic. You already know the "mathematics" at work in this chart.
The chart just tells you the "fancy names" for these different math facts.
Most of these properties are just common sense.
The first 13 properties are the most common, and need to be known by "name".
The remaining properties, referred to as the "equality properties of numbers",
will be used to explain steps when solving equations.
