Universal Algebra/Definitions, examples

Recall that whenever $S$ is a set, then $𝒯(S)$ is the class of all $S$-tuples, regardless of size.

Note that in this definition, $\alpha =\{()\}$ (the set consisting only of the empty tuple) is allowed, so that in this case, $\circ$ can be identified with a constant in $A$. It is customary to regard $0$-ary operations as constants in $A$.

For example, if we have a subset of a group that contains the identity and is closed under inversion and the product (that is, if we have a subset of a group that is closed under the 0-ary, the 1-ary and the 2-ary operation), then that subset is a subgroup.