1. Sets, numbers, and variables Flashcards
Does the order of elements within the braces matter?
No. S = {a, b, c} = {b, a, c}
What is a SET?
A collection of objects called ELEMENTS, that are listed within braces, { }.
What is the set having no elements called?
The EMPTY SET { } or NULL SET (circle with slash).
What is a SUBSET?
If each element of set B is also an element of set A, then set B is a subset of A.
B = {2, 4} ; A = {1, 2, 3, 4, 5}
Set B is a SUBSET of A.
What is the set of NATURAL NUMBERS?
{1, 2, 3, …}
What is the set of WHOLE NUMBERS?
{0, 1, 2, 3, …}
What is the set of INTEGERS?
{… -3, -2, -1, 0, 1, 2, 3, …}
What is the set of RATIONAL NUMBERS?
The set of all numbers that can be written as fractions in which their numerators and denominators are integers.
Name three subsets of rational numbers.
Natural numbers, whole numbers, and integers.
How are RATIONAL NUMBERS represented by decimals?
They can be written as nonending, repeating decimal numbers in which a set of one or more digits endlessly repeat. 3/11 = 0.272727…
What type of number does a repeating decimal represent?
A RATIONAL NUMBERS.
What set of numbers cannot be expressed as the quotient of two integers?
IRRATIONAL NUMBERS such as pi and the square root of 2.
What are nonending decimal numbers in which there is no repeating pattern of the same sequence of digits called?
IRRATIONAL NUMBERS
Is 0.13133133313333… a rational or irrational number?
Irrational number.
Is 0.666666…. a rational or irrational number?
Rational number.
What two sets combine to make the set of REAL NUMBERS?
The set of rational numbers combined with the set of irrational numbers.
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.
REAL NUMBER LINE.
What is one-to-one correspondence?
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.
What is the COORDINATE of a point?
The real number that is paired with the point.
What is a VARIABLE?
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.
What is a CONSTANT?
Unlike a variable, a constant has a fixed value. In the sum x + 8, 8 is a constant.
What is GENERALIZING IN ALGEBRA?
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.
What is a PRODUCT?
The result of multiplying two or more FACTORS together.
