T2: Language and Symbols Flashcards
CHARACTERISTICS OF THE LANGUAGE OF MATHEMATICS
o Precise
o Concise
o Powerful
the mathematical analogue of a ‘noun’
Expression
the mathematical analogue of a ‘sentence’
Sentence
It is the object that is being worked on by an operation
OPERAND
objects that are manipulated
Operands
symbols that represent specific actions
Operators
operation is performed on one operand
Unary
operation is performed on two operands
Binary
The product and the sum of any two real numbers is also a real number
Closure of Binary Operations
A binary operation is said to be commutative if a change in the order of the arguments results in equivalence
Commutativity of Binary Operations
A binary operation is said to be associative if parentheses can be reordered and the result is equivalent
Associativity of Binary Operations
Distributivity applies when multiplication performed on a group of two numbers added or subtracted together
Distributive Property of Binary Operations
An element 𝑒 is said to be an identity element (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 inverse denoted 𝑥 −1 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
