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Natural Numbers
Where do the natural numbers start?
1
Write them in set notation
{1, 2, 3, . . . }
Whole Numbers
Where do the whole numbers start?
0
Write them in set notation
{0, 1, 2, 3, . . . }
Integers
Define integers using whole numbers
Whole numbers and their opposites
Write in set notation
{. . . -3, -2, -1, 0, 1, 2, 3, . . . }
Rational Numbers
Define rational numbers using integers
A ratio of two integers, but the denominator cannot be
zero
Write in set building notation
Irrational Numbers
Define irrational numbers using rational numbers
Numbers that are not rational
Most common examples
Square roots, radicals
Real Numbers
Define real numbers using rational and irrational
numbers.
Any number that is rational or irrational
Define real numbers using the phase “number line”
Any number that is on a number line
Imaginary Numbers
What is an imaginary number?
A number that has an i in it.
What is i?
Square root of -1
Complex Numbers
All real numbers are complex numbers
All imaginary numbers are complex numbers
In general, any number of the form a + bi
where a is the real part
and bi is the imaginary part
Give a number that is a whole
number but not natural number.
0
Give a number that is an integer
but not a whole number
-4
Give a rational number that is not
an integer
What Property is this?
5+3=3+5
Commutative Property of
Addition
7+0=7
Additive Identity Property
5(a + b) = 5a + 5b
Distributive Property
Additive Inverse Property
5 + (x + y) = (5 + x) + y
Associative Property of Addition
Multiplicative Inverse Property
8x = 8x
Reflexive Property of Equality