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- StudyBlue
- Wisconsin
- University of Wisconsin - Madison
- Mathematics
- Mathematics 114
- Lino Amorim/nenciu
- Lecture 1 part 1

Nick G.

Natural Numbers

1, 2, 3, 4...

Whole Numbers

0, 1, 2, 3, 4...

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Integers

-4, -3, -2, -1, 0, 1, 2, 3, 4...

Rational Numbers

x=a/b, where b are integers and b is not zero.

Any integer m can be written as m/1, thus...

All integers are rational numbers.

Irrational numbers

Includes any real numbers that is not a rational number.

pi = 3.14159265

Square root of 2 = 1.41...

pi = 3.14159265

Square root of 2 = 1.41...

Give an example of a rational number with repeating terminating decimals.

1/3 = 0.3333

0.9 = 1.0 = 1

0.9 = 1.0 = 1

Real numbers

The rational and irrational numbers together.

Operations on the set of real numbers:

Addition...

Multiplication...

Addition...

Multiplication...

Addition: a+b

Multiplication: a x b

Multiplication: a x b

Commutative Property

a+b = b+a

a x b = b x a

a x b = b x a

Associative Property

(a+b)+c = a+(b+c)

(a x b)c = a(b x c)

(a x b)c = a(b x c)

Distributive Property

a(b+c) = a x b+ a x c

Identity Property

Additive identity

Multiplicative identity

Additive identity

Multiplicative identity

additive identity: a+0 = 0+a = a

multiplicative identity: a x 1 = 1 x a = a

multiplicative identity: a x 1 = 1 x a = a

Inverse Property

additive inverse

multiplicative inverse

additive inverse

multiplicative inverse

-a is the additive inverse of a: (-a)+a = 0

if b does not equal 0 then the multiplicative inverse of b is 1/b: b x 1/b = 1

if b does not equal 0 then the multiplicative inverse of b is 1/b: b x 1/b = 1

Multiplication by 0

a x 0 = 0 x a = 0

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If a x b = 0 then...

If a/b = 0 and b does not equal 0 then...

If a/b = 0 and b does not equal 0 then...

a = 0 or b = 0

a = 0

a = 0

a/0

Undefined

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