Summary Algebra Study Notes

Algebra
MATHEMATICS GRADE 12
NIKITA VERMEULEN

, ALGEBRA
THE NUMBER SYSTEM

Natural Numbers: N
Start at 1 and increase in ones up to infinity ().

Whole Numbers: N ο

Start at 0 and increase in ones up to infinity ().

Integers: Z

Integers extend whole numbers to include negative numbers.

Start at - and increase in ones up to + .

Rational Numbers:Q

Rational numbers are numbers which can be written:

 as a recurring decimal or,
 as a decimal that terminates or,
 as a fraction, where:
o the numerator and denominator have to be integers, and
o the denominator cannot be equal to zero.

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Examples of rational numbers are: ; 0, 3́; 0,75
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Irrational Numbers:Q '

Irrational numbers cannot be written in any of the forms of rational numbers.

Irrational numbers are non-recurring and non-terminating.

Examples of irrational numbers are: π ; √2 ; √3 9 ; 2,35408 …
 pi, and
 the square root of numbers that are not perfect squares or,
 cube roots of numbers that are not perfect cubes

Non-Real/Imaginary Numbers:

Occurs when you take the even root of a negative number.

Non-real numbers are known as complex numbers.

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Examples of non-real numbers are: √ −2 ; √ −9; 12√ −25


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