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The Language and Grammar of Mathematics - Coggle Diagram
The Language and Grammar of
Mathematics
Four Basic Concepts
Functions
it is a binary relation between to elements or variable. If f is a function, then the notation f (x) = y means
that f turns the object x into the object y.
Relations
it is a collection of ordered pairs containing one from each set. Make use of symbols like less than or greater than.
Sets
is a collection of objects which may be mathematical. Sets make use of parenthesis, brackets.
Binary Operations
calculations that combien two elements using mathematical operation. Some familiar examples are "plus", "minus", "times".
Introduction
Mathematical language is a system used by mathematicians to communicate mathematical ideas to one another. It differs from natural languages in that it aims to communicate abstract, logical ideas with precision and unambiguity. [1][2]
This language has a natural language substrate (for example, English), but it uses technical terms and grammatical conventions that are unique to it.
Some Elementary Logic
Quantifiers
Words like “all,” “some,” “any,” “every,” and “nothing” are called quantifiers, and in the English language
they are highly prone to this kind of ambiguity.
Negation
There is a symbol which means not and if p is any mathematical statement, then -p stands for the statement that is true and only p is not true
Logical Connectives
A logical connective is the mathematical equivalent of a
conjunction.
Free and Bound Variables
The letters t and v stand for real
numbers, and they are called variables