Algebra 2 Vocabulary

Deductive Reasoning

the process of applying rules - mathematics is this type of reasoning because there are mathematical rules yet to be discovered

Inductive Reasoning

the process of discovering rules - scientific endeavors are this type of reasoning; discovery of new mathematical relationships requires this type of reasoning

Numeral

a symbol or symbols used to express the idea of a number

Abstract

dealing with properties and ideas of things, just because they are things, regardless of feelings, emotions, and sensations we might connect with them; an idea that can describe an infinite number of concrete objects

Concrete

in mathematics, a word used to describe real objects - abstract ideas are always based on real things

Digit

any of the Hindu-Arabic numerals 1-9 and 0

Counting (Natural) Numbers

numbers used to count objects

Whole Numbers

counting numbers and the number 0

Integers

whole numbers and all negative numbers

Real Numbers

any number used to describe a positive or negative number; includes all integers, fractions, and decimals

Trichotomy Axiom

for any two real numbers a and b, exactly one of the following is true: a < b, a = b, a > b

Radical Sign

developed by Leonhard Euler in the 1700’s as a way to simplify the writing of factorial exponents

Square Root

if x is greater than 0, then the square root of x is the unique positive real number such that the square root of x squared is equal to ex

Imaginary Numbers

the result of taking the square root of a negative number

Complex Numbers

numbers that have a real part and an imaginary part, represented by a + bi, where i is Euler’s notation (the square root of -1)

X to the Power of 0 Equals 1

anything except 0 raised to the power of 0 equals 1

X to the -n Equals 1 Over X to the Power of n

anything except 0 raised to a negative power equals 1 over anything raised to the opposite of the power