We were discussing about the possibility of having an algebra over a field which is associative but has not the unity. Does it exist? It has been proposed as a counterexample the set of even numbers. We believe it is wrong because it can't be a vector space. If an associative but not unital algebra exists, how can we write its associative property? We usually write it as a commutative diagram or in terms of maps composition. In these terms the identity seams unavoidable. i.e. $$ m\circ\left(m\otimes id\right) = m\circ\left(id\otimes m\right)\qquad \text{associativity} $$ with $m : A\otimes A\to A$.