Multitude: Difference between revisions
(Created page with "'''Multitude''' is the quantity of a finite set. Synonyms for multitude are '''natural number''', '''whole quantity''', '''discrete quantity''', '''cardinality''', and the symbol <math>\mathbb{N}</math>; though all those concepts have different shades of meaning, Objective Mathematics uses them interchangeably. == Comparison == "Few" and "many" describe relative multitudes. == Counting == Counting is a process by which one identifies the isomorphism class of...") |
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'''Multitude''' is the [[quantity]] of a finite [[set]]. Synonyms for multitude are '''natural number''', '''whole quantity''', '''discrete quantity''', '''cardinality''', and the symbol <math>\mathbb{N}</math>; though all those concepts have different shades of meaning, Objective Mathematics uses them interchangeably. | '''Multitude''' is the [[quantity]] of a finite [[set]]. [TODO maybe circular because what do I mean by finite set?] Synonyms for multitude are '''natural number''', '''whole quantity''', '''discrete quantity''', '''cardinality''', and the symbol <math>\mathbb{N}</math>; though all those concepts have different shades of meaning, Objective Mathematics uses them interchangeably. | ||
== Comparison == | == Comparison == | ||
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== Counting == | == Counting == | ||
Counting is a process | '''Counting''' is a process in which one identifies the multitude of a set, through iteratively identifying multitudes of its subsets. | ||
== Specific natural numbers == | == Specific natural numbers == | ||
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== Addition == | == Addition == | ||
[ | '''Addition''' is a process in which one identifies the multitude of a [[Set#Disjoint union|disjoint union]], based his knowledge of the multitudes of its summands. (By the ''summands'' of a disjoint union <math>A \sqcup B</math>, I mean the set <math>A </math> and the set <math>B</math>.) | ||
== Multiplication == | |||
'''Multiplication''' is a process in which one identifies the multitude of a [[Sets#Cartesian product|cartesian product]], based on his knowledge of the multitudes of its summands. (By the ''summands'' of a cartesian product <math>A \times B</math>, I mean the set <math>A </math> and the set <math>B</math>.) | |||
Revision as of 03:17, 21 June 2024
Multitude is the quantity of a finite set. [TODO maybe circular because what do I mean by finite set?] Synonyms for multitude are natural number, whole quantity, discrete quantity, cardinality, and the symbol ; though all those concepts have different shades of meaning, Objective Mathematics uses them interchangeably.
Comparison
"Few" and "many" describe relative multitudes.
Counting
Counting is a process in which one identifies the multitude of a set, through iteratively identifying multitudes of its subsets.
Specific natural numbers
Multitude can be divided up into sub-concepts such as "1," "12," and "73."
Addition
Addition is a process in which one identifies the multitude of a disjoint union, based his knowledge of the multitudes of its summands. (By the summands of a disjoint union , I mean the set and the set .)
Multiplication
Multiplication is a process in which one identifies the multitude of a cartesian product, based on his knowledge of the multitudes of its summands. (By the summands of a cartesian product , I mean the set and the set .)
