Unit 1 Notes

Irrational Number

Numbers in which the decimal form never terminates and does not repeat. Common examples are n and non-perfect square roots.

Rational Numbers

Numbers in which the decimal form either terminates or repeats. Rational numbers can always be written as a fraction (a/b) where a and b are integers.

Integers

{...,-3, -2, -1,0, 1, 2, 3, ...}

Whole Numbers

{0, 1, 2, 3, 4, ...}

Natural Numbers

{1, 2, 3, 4, 5, ...}

Commutative Property

ADDITION EXAMPLE:MULTIPLICATION EXAMPLE:

Associative Property

ADDITION EXAMPLE:MULTIPLICATION EXAMPLE:

Identity Property

ADDITION EXAMPLE:MULTIPLICATION EXAMPLE:

Inverse Property

ADDITION EXAMPLE:MULTIPLICATIONN EXAMPLE:

Distributive Property

ADDITION EXAMPLE:MULTIPLICATION EXAMPLE:`

Closure Property

A set is closed (under an operation) if the operation always produces an element of the same set. If an element outside the set is produced, then the operation is not closed.

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Integers are closed under multiplication.

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Irrational numbers are closed under subtraction.

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Whole numbers are closed under division.

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Odd numbers are closed under addition.

GEMDAS

1. grouping symbols; 2. exponents; 3. multiplication and division; 4. addition and subtraction

Isolate

The absolute value expression.

Create Two Cases

The set "inside" equal too both the positive and negative value of the number on the opposite side of the equal sign.

Solve

Both equations.

Check

For extraneous solutions.

Interval Notation

A way to write the solution to an inequality using infinity symbols, parentheses, and brackets.

Set Notation

Another way of expressing the solution to an inequality.