Complex numbers
Have the form a + bi, where a and b are real and i = √-1ex) 2 - 3i, 7, root 3, and root of -5
Real numbers
Have points on the number line. (Complex)ex) 3, -17.4, root 5, pi, 4/3
Imaginary numbers
Square roots of negative numbers. Have no points on the number line. (Complex)ex) root -3, 5 root -2, - of root -9
Positive numbers
Numbers that are greater than zero. (Complex, real)ex) 0.001, 37, root 15
Zero
Neither positive nor negative. (Complex, real)ex) 0
Negative numbers
Numbers less than 0. (Complex, real)ex) -7.5, -58, - of root 3
Rational numbers
Can be expressed exactly as a ratio of two integers. (Complex, real)ex) 4/5, -2/3, 7.31, -5
Irrational numbers
Cannot be expressed exactly as a ratio of two integers, but are real numbers. (Complex, real)ex) root 5, - of 3 root 11, pi
Radicals
Involve square root, cube root, etc. of integers (Complex, real, irrational)ex) root 5, - of 3 root 11
Transcendental numbers
Cannot be expressed as roots of integers. (Complex, real, irrational)ex) pi
Integers
Whole numbers and their opposites. (Complex, real, rational)ex) 2, -17, 2001, 0)
Nonintegers
Fractions: numbers between the integers. (Complex, real, rational)ex) 3/4, 1 2/7, -4.63
Natural numbers
Positive integers or counting numbers. (Complex, real, rational, integers)ex) 2, 2001
Digits
numbers from which the numerals are made (Complex, real, rational, integers)ex) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Even numbers
Integers divisible by 2. (Complex, real, rational, integers)ex) 2046, -38, 562, 0
Odd numbers
integers not divisible by 2. (Complex, real, rational, integers)ex) -49, 15, 2001, 1
axioms
What are some properties that are accepted without proof and are used as starting points for working numbers?
closure
What is it called when real numbers are closed under addition and multiplication? ex. 0x1=1 not closed 1+1=2
commutativity
What is it called when x + y = y + x or xy = yx?
associative
What is it called when if (x+y)+z = x+ (y+z)?
Distributive
What is it called when x+ (y+z) = xy+xz?
identity elements
What is it called when x+0=x or y x 1 = y?
inverse
What is it called when you have x + (-x)=0 or when y x 1/y = 1?
Variable
A letter which stands for an unspecified number from a given set.
expression
What is a collection of variables and constants connected by operation signs, which stands for a number?
Polynomial
Algebraic expressions that involve only the operations of addition, subtraction, and multiplication of variables. (No absolute values, division, or square roots)
monomial
What is only one number of terms in the equation?
binomial
What is a polynomial with two terms called?
trinomail
What is a polynomial with three terms called?
constant
What is a variable with no degree called?
linear
What is a variable with one degree?
Quadratic
What is a variable squared called?
cubic
What is a variable that is cubed called?
Quartic
What is a variable that is raised to the fourth power called?
Quintic
What is a variable that is raised to the fifth power called?
6th degree
Which degree doesn't have a special name?
extraneous solution
a number which satisfies a transformed equation, but not the original equation
Reflexive Property
if x is a real number, x=x
Symmetry Property
If x=y, then y=x
Transitive Property
For equality, if x=y and y=z, then x=zFor order, if x<y and y<z, then x<z
Trichotomy Property
If x and y are two real numbers, then exactly one of the following must be true.y<xy>xy=x