Speakur

Word Pronunciation & Dictionary

natural numbers object

Word Rarity Uncommon

Frequency: Zipf frequency 4.34 in modern English

Syllables
nat-u-ral num-ber-s ob-ject
IPA
35
Scrabble Score
20
Letters
6
Syllables
13
Unique Chars

Meaning

noun

An object which has a distinguished global element (which may be called z, for “zero”) and a distinguished endomorphism (which may be called s, for “successor”) such that iterated compositions of s upon z (i.e., sⁿ∘z) yields other global elements of the same object which correspond to the natural numbers (sⁿ∘z↔n). Such object has the universal property that for any other object with a distinguished global element (call it z’) and a distinguished endomorphism (call it s’), there is a unique morphism (call it φ) from the given object to the other object which maps z to z’ (ϕ∘z=z') and which commutes with s; i.e., ϕ∘s=s'∘ϕ.

Inflected Forms

natural numbers objects (plural)

Questions

What does natural numbers object mean?
An object which has a distinguished global element (which may be called z, for “zero”) and a distinguished endomorphism (which may be called s, for “successor”) such that iterated compositions of s upon z (i.e., sⁿ∘z) yields other global elements of the same object which correspond to the natural numbers (sⁿ∘z↔n). Such object has the universal property that for any other object with a distinguished global element (call it z’) and a distinguished endomorphism (call it s’), there is a unique morphism (call it φ) from the given object to the other object which maps z to z’ (ϕ∘z=z') and which commutes with s; i.e., ϕ∘s=s'∘ϕ.

How to pronounce natural numbers object

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