In the sense of 'universal algebra':(adsbygoogle = window.adsbygoogle || []).push({});

The natural numbers N can be presented as an free algebra with one constant (0) and one -unary- operation s(x) (i.e. x --> x+1). We have (of course) elements 0, s(0), s(s(0)), etc...

Is there a good name for a set A with one constant (*) and one -binary- operation b? Here one term is b(b(*,*),b(b(*,*),*)), which can be visualized as some sort of unlabeled binary tree.

Unfortunately, there are multiple concepts related to the term binary tree (see Wikipedia, for example). Here for example, every node must have 0 or 2 children, not 0, 1 or 2 as is commonly allowed. Plus there is the distinction between combinatorial objects and their algebraic forms.

Hopefully there is something more common than "Free (2,0)-algebra [over the empty set]".

Skolem

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Terminology: free algebra with binary op, constant.

**Physics Forums | Science Articles, Homework Help, Discussion**