Mathematical Languange And Symbols Flashcards
Mathematics In The Modern World Prelims Exam
It facilitates communication and clarifies meaning.
Language of Mathematics
It allows people to express themselves and maintain their
identity
Language of Mathematics
Characteristics of the Language of Mathematics
The language of mathematics makes it easy to express the
kinds of thoughts that mathematicians like to express. It is:
- Precise
- Concise
- Powerful
Mathematical Symbols
Σ
the sum of
Mathematical Symbols
Ǝ
there exists
Mathematical Symbols
ꓯ
for every (for any)
Mathematical Symbols
Є
element of
Mathematical Symbols
⊆
subset of
Mathematical Symbols
⇒
if …., then
Mathematical Symbols
⇔
if and only if
Mathematical Symbols
ℛ or ℜ or ℝ
set of real numbers
Mathematical Symbols
ℕ
set of natural numbers
Mathematical Symbols
ℤ
set of integers
Mathematical Symbols
ℚ
set of rational numbers
In English, ________ are used to name things we want to talk about (like people, places, and things); whereas sentences are used to state complete thoughts.
Nouns
- A typical English sentence has at least _______ , and at least _____.
One noun
One Verb
MATHEMATICS: expressions versus sentences
The mathematical analogue of a ‘noun’ will be called an __________
Expression
it is a name given to a mathematical object of interest.
Expression
- The mathematical analogue of a ‘sentence’ will also be called a _________.
Sentence
‘=‘ is
Verb
The ________ is the object that is being worked on by an operation.
Operand
___________ can be mathematical ones such as multiplication or
addition, or they can be more sophisticated functions.
Operations
Operations can be mathematical ones such as ______________ or _____________, or they can be more ____________ functions.
Multiplication
Addition
Sophisticated
In all computer languages, expressions consist of two types of components:
Operators
Operands
________ are the objects that are manipulated
Operands
__________ are the symbols that represent specific actions.
Operators
5 + x
x and 5 are __________
+ is an ________
Operands
Operators
Types of Operators
Unary
Binary
It means operation performed on one operand
Unary
It means operation is performed on two operands
Binary
is an operation with only one operand, i.e. a single input.
Unary operation
are prefix notation (e.g. +, −, ¬), postfix notation (e.g. factorial n!), functional notation (e.g. sin x or sin(x)), and superscripts (e.g. transpose AT). Other notations exist as well.
Common notations
In common arithmetic,
the unary operators are:
negation
reciprocal
absolute value
____________ involves reversing the sign of a number.
Negation
it involves dividing 1 by the number.
Reciprocal
The _____________ involves reversing the sign of a number if it is
negative, and leaving the number unchanged if it is 0 or positive.
Absolute value
a set is a calculation that combines two elements of the set (called________) to produce another element of the set.
Binary operation
Operands
a______________ is an operation of parity (the number of arguments or operands that the function takes) of two whose two _____ and one _________ are the same set.
binary operation
domains
codomain
PROPERTIES OF BINARY OPERATIONS
- Closure of Binary Operations
- Commutativity of Binary Operations
- Associativity of Binary Operations
- Distributivity of Binary Operations
- Identity Elements of Binary Operations
- Inverses of Binary Operations
A Binary Operations that product and the sum of any two real numbers is also a real number. In symbols, we write
Closure of Binary Operations
What binary operation is said to be ________ if a change in the order of the arguments results in equivalence?
Commutativity of Binary Operations
Commutative
What binary operation is said to be ________ if parentheses can be reordered and the result is equivalent?
Associative
Associativity of Binary Operations
________________applies when multiplication is performed on a group of two numbers added or subtracted together
Distributivity of Binary Operations
An element “e” is said to be an ____________ (or neutral element) of a binary operation if under the operation any element combined with “e” results in the same element.
Identity Elements of Binary Operations
For an element x, the ____ denoted x1 when combined with x under the binary operation results in the identity element for that binary operation.
Inverses of Binary Operations
is an instrument for appraising the correctness of reasoning.
Logic
is a declarative statement that is true or false but not both.
proposition P
is a table that shows the truth value of a compound statement for all possible truth values of its simple statements.
Truth Table
it is if the word is not introduced in the negative statement.
NEGATION
A word or symbol that joins two sentences to produce a new one.
LOGICAL CONNECTIVES
