natural numbers object

1. 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.

1. Gravity is the natural force by which objects are attracted to each other.

   Гравітація це природна сила, через яку речі взаємопритягаються. — marko

   deGravitation ist die Naturkraft, mit der sich Gegenstände gegenseitig anziehen. — MUIRIEL

   CK · Tatoeba · CC BY 2.0 FR · B1Open on TatoebaReport a problem

2. There are many natural objects that we can put to use.

   AlanF_US · Tatoeba · CC BY 2.0 FR · B1Open on TatoebaReport a problem

3. All natural objects and phenomena used to be considered as having kami, so the gods of Shinto were uncountably numerous.

   yurusu · Tatoeba · CC BY 2.0 FR · C2Open on TatoebaReport a problem

regular