Mathematics in the Modern World Reviewer Flashcards

Vocabulary flashcards generated from lecture notes covering math as a language, sets, number types, functions, properties of real numbers, logic statements, quantifiers, reasoning methods, data types, and levels of measurement.

Fibonacci Sequence

A sequence credited to Leonardo Pisano consisting of numbers such as $0, 1, 1, 2, 3, 5, 8$.

Math as a Precise Language

A characteristic of mathematical language where ideas are stated exactly, such as converting "I have a few apples" to "$\text{Apples} = 2$".

Math as a Concise Language

A characteristic of mathematical language where ideas are stated briefly, such as writing "Take length & multiply by width to get area" as $A = l \times w$.

Math as a Powerful Language

A characteristic of mathematical language where complex ideas are expressed simply, such as writing "Pushing harder makes things go faster" as $F = m \times a$.

Mathematical Expression

An incomplete mathematical sentence that does not contain an equals sign ($=$), such as $5+2$.

Mathematical Sentence

A complete mathematical thought that contains an equals sign ($=$), such as $5+2 = 7$.

Set

A whole list of items, denoted as a collection such as $P = \{\text{Mercury}, \text{Mars}, \text{Penis}\}$.

Element

A singular item in a set, represented by the symbol $\in$, such as $\text{Mercury} \in P$.

Subset

A contained item or group of items within a set, represented by $\subseteq$, such as {\text{Mercury}, \text{Penis}} $\subseteq P$.

Natural Numbers

Whole numbers only, ranging from $0$ to $5\dots$

Integer Numbers

Whole numbers combined with negative numbers, ranging from $-5$ to $5\dots$

Decimal Numbers

Whole numbers and negative numbers that include decimals.

Rational Numbers

Any numbers that can be turned into fractions.

Irrational Numbers

Any numbers that cannot be turned into fractions.

Function

A relation consisting of a set of ordered pairs with a domain ($D$) and range ($R$) where the domain values do not repeat.

Commutative Property of Real Numbers

A property of real numbers involving swapping terms, defined by $a+b = b+a$.

Associative Property of Real Numbers

A property of real numbers involving regrouping terms, defined by $(a+b)+c = a+(b+c)$.

Distributive Property of Real Numbers

A property of real numbers involving spreading terms across addition, defined by $a(b+c) = a(b)+a(c)$.

Identity Property of Real Numbers

A property of real numbers where a value remains unchanged, defined by $a+0 = a$.

Inverse Property of Real Numbers

A property of real numbers where a term cancels itself out, defined by $a+(-a) = 0$.

Logic

Valid reasoning and common sense.

Statement

A sentence that is answerable by only TRUE or FALSE.

Simple Statement

A statement expressing one single idea, such as "Apple is red."

Compound Statement

A statement expressing two or more ideas joined by connective words, such as "Apple is red and Mark is baho."

Conjunction

A compound statement formed using the connective "and", represented by the symbol $\wedge$.

Disjunction

A compound statement formed using the connective "or", represented by the symbol $\vee$.

Conditional Statement

A compound statement formed using the connective "if… then", represented by the symbol $\rightarrow$.

Biconditional Statement

A compound statement formed using the connective "if and only if", represented by the symbol $\leftrightarrow$.

Existential Quantifier

A quantifier stating that there exists at least one item, denoted by $\exists$, such as "There exist a student who likes MATH".

Universal Quantifier

A quantifier applying to all or every item, denoted by $\forall$, such as "All apples are red".

Negation

A statement that negates or presents the opposite of a statement, such as turning "It is raining" into "It is NOT raining."

Inductive Reasoning

Reasoning based on observing patterns to move from specific observations to general conclusions, such as $0, 1, 1, 2, 3, 5, 8\dots 13!$

Deductive Reasoning

Reasoning based on rules, cases, and conclusions to move from general statements to specific conclusions.

Quantitative Data

Data involving amounts, numerical values, or measurements.

Qualitative Data

Data involving labels or categories.

Discrete Quantitative Data

Quantitative data consisting of countable whole numbers.

Continuous Quantitative Data

Quantitative data involving measurements and decimals.

Nominal Level of Measurement

A level of measurement for data that has no inherent order.

Ordinal Level of Measurement

A level of measurement for data that is ranked.

Interval Level of Measurement

A level of measurement where zero has a purpose, such as $0^\circ$.

Ratio Level of Measurement

A level of measurement where zero exists but has no purpose.