Mathematical Language & Symbols Flashcards
What is language?
A systematic means of communicating ideas or feelings by the use of conventional symbols, sounds, or marks having understood meaning.
∀ represents…
“for every”.
∃ represents…
“there exists”.
∴ represents…
“therefore”.
It is a group of words that expresses a concept.
Phrase.
It is a group of words that are put together to mean something.
Sentence.
It is a group of numbers or variables with or without mathematical operation.
Expression.
It is a group of numbers or variables with or without mathematical operation separated by an equal sign
Equation.
It is a group of numbers with or without mathematical operation separated by an equal sign.
Equation.
What is precise?
It is when you are able to make very fine distinctions.
What is concise?
It is when you are able to say things briefly.
What is powerful?
It is when you are able to express complex thoughts with relative ease.
What are the 3 characteristics of a mathematical language?
Precise, concise, and powerful.
A __ is a collection of objects called as elements.
set
The format sets usually follow.
Roster Method.
“1 ∈ S” means…
1 is an element of set S.
“9 ∉ S” means…
9 is not an element of set S.
Turn into Set-builder Notation: S contains all x’s such that x is greater than or equal to 0 AND
x is less than or equal to 1.
S = {x|x ≥ 0 AND x ≤ 1}.
Empty sets can be represented by…
∅ or {}.
The set of natural numbers can be represented by…
ℕ = {1, 2, 3, 4, 5, …}.
The set of integers can be represented by…
ℤ = {…, −2, −1, 0, 1, 2, …}.
It is the symbol for a subset.
⊆.
∅ ⊆ {1, 2, 3, 4}.
True.
∅ ⊆ {1, 2, 3, 4}.
True.
{1,2,3,4,5} ⊆ {1,2,3,4,5}.
True.
A represents…
any set.
A’ represents…
the complement of set A.
Set __ contains
elements in the universal set which are not contained in set __.
A’, A
The union of sets A and B, denoted by__, is the
set that contains all the elements that belong to A, B, __ both.
U, or
Using the roster method how would you express the union of sets.
A U B = {x|x ∈ A or x ∈ B}.
The intersection of sets A and B, denoted by __, is the set of elements common to both A __ B.
∩, and
Using the roster method how would you express the intersection of sets.
A ∩ B = {x|x ∈ A and x ∈ B}.
