Section 1.1 Real Numbers

Front

Define Real Numbers.

Back

Real numbers include all the numbers on the number line, encompassing rational numbers (like integers and fractions) and irrational numbers (like square roots of non-perfect squares).

Front

What is the Union of Sets?

Back

The union of two sets A and B, denoted as A ∪ B, is the set of elements that are in A, in B, or in both.

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What is the Associative Property?

Back

The associative property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. For example, (a + b) + c = a + (b + c).

Front

What is a Rational Number?

Back

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where p is the numerator and q is the non-zero denominator.

Front

What is an Interval Notation?

Back

Interval notation is a way of writing subsets of the real number line. It uses parentheses and brackets to denote whether endpoints are included or excluded.

Front

What is the Absolute Value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you simplify fractions?

Back

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).

Front

What is the Distributive Property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

What is the Commutative Property?

Back

The commutative property states that the order in which two numbers are added or multiplied does not change the result. For example, a + b = b + a.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include its endpoints a and b, while a closed interval [a, b] includes both endpoints.