Vocabulary List for MAT-109 UNIT A Chapters 1, 2 and 6

The distance a number is from zero on a number line, always positive or zero. Example: |−5| = 5

Absolute Value:

Numbers that tell how many elements are in a set. Example: The set {a, b, c} has cardinal number 3.

Cardinal Numbers:

All elements in the universal set except those in the empty set — so it's the entire universal set.

Complement of an Empty Set:

All elements in the universal set that are NOT in a given set. Example: If universal set is {1,2,3,4} and set A = {1,2}, then A's complement = {3,4}.

Complement of a Set:

The empty set, because there are no elements outside the universal set.

Complement of a Universal Set:

A whole number greater than 1 that has more than two factors. Example: 4, 6, 8 (not prime).

Composite Number:

An idea or statement believed to be true but not yet proven.

Conjecture:

An example that proves a conjecture false.

Counterexample:

Reasoning from general rules to reach a specific conclusion.

Deductive Reasoning:

A table showing the differences between terms in a sequence to find patterns.

Difference Table:

A method to determine if one number divides evenly into another without remainder.

Divisibility Test:

A number that divides another number exactly (without remainder).

Divisor:

The objects or numbers contained in a set.

Elements of a Set:

Three dots (...) showing a sequence continues.

Ellipsis:

A set with no elements, symbol: ∅ or {}

Empty Set:

Two sets that have exactly the same elements.

Equal Sets:

Two sets that have the same number of elements (cardinality), but not necessarily the same elements.

Equivalent Sets:

Writing a number to show the value of each digit. Example: 345 = 300 + 40 + 5

Expanded Form:

A number that divides another number exactly.

Factor:

A sequence where each number is the sum of the two before it: 0,1,1,2,3,5,8...

Fibonacci Sequence:

Having a limited number of elements.

Finite:

Every integer greater than 1 can be written uniquely as a product of prime factors.

Fundamental Theorem of Arithmetic:

Making a general conclusion based on observing many specific examples.

Inductive Reasoning:

Number of subsets excluding the set itself. For a set with n elements: 2ⁿ - 1 proper subsets.

Number of Proper Subsets of Sets:

Total subsets including empty set and the set itself. For a set with n elements: 2ⁿ subsets.

Number of Subsets of Sets:

The branch of math dealing with properties and relationships of numbers, especially integers.

Number Theory:

The value of a digit depending on its position in a number.

Place Value:

Writing a number as a product of prime numbers.

Prime Factorization:

A number greater than 1 with exactly two factors: 1 and itself.

Prime Number:

A subset that is not equal to the original set (it has fewer elements).

Proper Subset of a Set:

An ordered list of numbers or objects.

Sequence:

A collection of distinct objects or numbers.

Set:

A set where every element is also in another set.

Subset of a Set:

The set containing all possible elements under consideration.

Universal Set:

A visual way to show relationships between sets using overlapping circles.

Venn Diagram:

A set with clear rules so it's obvious if an object belongs or not.

Well-Defined Set: