Flashcards: Mathematical Language and Sets — 33 cards

What is mathematical language?

A system of conventional spoken, manual, or written symbols used to express ideas.

What kind of content does mathematical language carry?

It carries no emotional content.

Is mathematical language temporal or non-temporal?

Mathematical language is non-temporal.

How is mathematical language described in terms of precision and conciseness?

It is precise and concise.

What is a mathematical expression?

A group of characters or symbols representing a quantity and/or an operation.

What does an algebraic expression contain?

Numbers, variables represented by letters, and operations like addition or subtraction.

What defines a mathematical sentence?

An expression that is either true or false.

What distinguishes an open mathematical sentence?

It may be true or false depending on unknown values.

What characterizes a closed mathematical sentence?

It is already known to be true or false.

Is 3 + 12 = 15 a true or false closed mathematical sentence?

It is a true closed mathematical sentence.

Is 3 + 12 = 312 a true or false closed mathematical sentence?

It is a false closed mathematical sentence.

Which words imply addition in mathematical language?

Plus, the sum of, increased by, total, more than, and added to imply addition.

Which words imply subtraction in mathematical language?

Minus, the difference of, decreased by, fewer than, less than, and subtracted from imply subtraction.

Which words imply multiplication in mathematical language?

Times, the product of, multiplied by, and of imply multiplication.

Which words imply division in mathematical language?

Divided by, the quotient of, and per imply division.

What does a sentence express in English?

A sentence expresses a fact or fiction in English.

What does a sentence express in mathematics?

A sentence expresses a true or false statement in mathematics.

What is a set in mathematics?

A collection of common objects, numbers, letters, people, or other sets.

What defines a subset of a set?

Every element of the subset is found in another set.

What does cardinality of a set represent?

The number of elements in the set.

How does the roster method represent a set?

By listing or enumerating its elements.

How does the rule method describe a set?

By specifically describing elements using set-builder notation.

What distinguishes a finite set from an infinite set?

A finite set has a limited number of elements; an infinite set does not.

What is a universal set and its notation?

A set containing all elements found in other given sets, denoted by U.

What defines an empty set, equal sets, and equivalent sets?

An empty set has no elements; equal sets have exactly the same elements; equivalent sets have the same cardinality.

What elements does the union of two sets contain?

All elements in either set.

Why is set union commutative?

Because A union B equals B union A.

What elements does the intersection of two sets contain?

All elements common to both sets.

Why is set intersection commutative?

Because A intersection B equals B intersection A.

What elements does the complement of set A contain?

All elements in the universal set not in A.

What elements does the difference of A and B contain?

Elements in A but not in B.

What elements does the symmetric difference of A and B contain?

Elements in A or B but not both.

What does the Cartesian product A times B consist of?

Ordered pairs with A element first and B element second.