Chapter 1
Advanced Algebra
Terms
undefined, object
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- inequality
- a sentence that contains <, >, greater/less than or equal to symbols
- real numbers
- those numbers that can be represented by decimals
- conjecture
- educated guess
- theorems
- a postulate/definition proved
- sequence
- an ordered list
- model for an operation
- a pattern that describes many of the uses of that operation
- open sentence
- a sentence that may be true or false depending on what values are substituted for the variables
- subscript/index
- a number or variable written below and to the right of a variable
- nth term
- the equation that allows any number of a sequence to be found
- rational numbers
- those numbers that can be represented by fractions
- postulates/definition
- statements assumed to be true in a mathematical system
- less than
- x-y
- replacement set/domain
- set of meaningful numbers or things that can be substituted for a variable
- integers
- {0,1,-1, 2, -2...}
- equivalent sentences
- sentences with the same solutions
- interval
- a solution to an inequality of the form that involves symbols that can be replaced
- greater than
- >
- algebraic expression
- when numbers and variables are combined
- subscripted variables
- a number or variable indicating the position a number falls in a sequence of numbers
- whole numbers
- {0,1,2,3...}
- evaluating an expression
- substituting for the variables and calculating a result
- term
- each item on the list of a sequence
- solution
- values that make a sentence true
- properties
- postulates, theorems, definitions
- explicit formula for the nth term
- t sub n=((n+1)(n+2))/2
- is less than
- <
- less
- y-x
- positive real numbers
- those real numbers greater than zero
- formula
- a sentence stating that a single variable is equal to an expression with one or more variables on the other side
- equation
- a sentence stating that two expressions are equal
- recursive formula/definition
- a. indicates the first term b. gives a rule for how he nth term is related to one or more of the previous terms
- variable
- a symbol that can be replaced by any one of a set of numbers or other objects
- counterexample
- an example that proves a conjecture to be wrong
- natural numbers/counting numbers
- {1,2,3,4...}