1. Sets, numbers, and variables

Question 1

Does the order of elements within the braces matter?

Answer 1

No. S = {a, b, c} = {b, a, c}

Question 2

What is a SET?

Answer 2

A collection of objects called ELEMENTS, that are listed within braces, { }.

Question 3

What is the set having no elements called?

Answer 3

The EMPTY SET { } or NULL SET (circle with slash).

Question 4

What is a SUBSET?

Answer 4

If each element of set B is also an element of set A, then set B is a subset of A.

Question 5

B = {2, 4} ; A = {1, 2, 3, 4, 5}

Answer 5

Set B is a SUBSET of A.

Question 6

What is the set of NATURAL NUMBERS?

Answer 6

{1, 2, 3, …}

Question 7

What is the set of WHOLE NUMBERS?

Answer 7

{0, 1, 2, 3, …}

Question 8

What is the set of INTEGERS?

Answer 8

{… -3, -2, -1, 0, 1, 2, 3, …}

Question 9

What is the set of RATIONAL NUMBERS?

Answer 9

The set of all numbers that can be written as fractions in which their numerators and denominators are integers.

Question 10

Name three subsets of rational numbers.

Answer 10

Natural numbers, whole numbers, and integers.

Question 11

How are RATIONAL NUMBERS represented by decimals?

Answer 11

They can be written as nonending, repeating decimal numbers in which a set of one or more digits endlessly repeat. 3/11 = 0.272727…

Question 12

What type of number does a repeating decimal represent?

Answer 12

A RATIONAL NUMBERS.

Question 13

What set of numbers cannot be expressed as the quotient of two integers?

Answer 13

IRRATIONAL NUMBERS such as pi and the square root of 2.

Question 14

What are nonending decimal numbers in which there is no repeating pattern of the same sequence of digits called?

Answer 14

IRRATIONAL NUMBERS

Question 15

Is 0.13133133313333… a rational or irrational number?

Answer 15

Irrational number.

Question 16

Is 0.666666…. a rational or irrational number?

Answer 16

Rational number.

Question 17

What two sets combine to make the set of REAL NUMBERS?

Answer 17

The set of rational numbers combined with the set of irrational numbers.

Question 18

What is a “pictorial representation of the set of REAL NUMBERS that resembles a ruler-like line on which an arbitrary point, called the ORIGIN, is labeled 0.

Answer 18

REAL NUMBER LINE.

Question 19

What is one-to-one correspondence?

Answer 19

The set of real numbers and the set of points on a line can be paired such that each real number corresponds exactly to one point on the line and each point on the line corresponds to one real number.

Question 20

What is the COORDINATE of a point?

Answer 20

The real number that is paired with the point.

Question 21

What is a VARIABLE?

Answer 21

A symbol that serves as a placeholder for an unknown member of a given set, called the REPLACEMENT SET or the DOMAIN of the variable.

Question 22

What is a CONSTANT?

Answer 22

Unlike a variable, a constant has a fixed value. In the sum x + 8, 8 is a constant.

Question 23

What is GENERALIZING IN ALGEBRA?

Answer 23

Mathematical laws and properties that apply to all members of a set of numbers can be concisely stated using variables. For example “a + b = b + a” states that the order in which any two real numbers are added does not matter.

Question 24

What is a PRODUCT?

Answer 24

The result of multiplying two or more FACTORS together.