Speakur

Word Pronunciation & Dictionary

finitely generated

Word Rarity Very rare

Frequency: Zipf frequency 2.30 in modern English

Syllables
finite-ly -gen-er-at-ed
IPA
25
Scrabble Score
17
Letters
6
Syllables
11
Unique Chars

Meaning

adj

In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

adj

In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

adj

In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

adj

In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

adj

In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

Etymology

From the study of generators. The motivation for calling topologies satisfying sense 1.5 "finitely generated" is that any topology satisfies sense 1.5 if and only if it is coherent with its finite subspaces. Thus, metaphorically, it is "generated" by them. The category-theoretic senses were created to generalize those of abstract algebra, and so were named identically.

Questions

What does finitely generated mean?
In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:
Where does finitely generated come from?
From the study of generators. The motivation for calling topologies satisfying sense 1.5 "finitely generated" is that any topology satisfies sense 1.5 if and only if it is coherent with its finite subspaces. Thus, metaphorically, it is "generated" by them. The category-theoretic senses were created to generalize those of abstract algebra, and so were named identically.

How to pronounce finitely generated

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