Would it be correct to call mixture of three chemical solutions, namely salt water, salt water with sodium hydroxide, and salt water with HCl, a group? As I understand this, (which is not entirely realistic) mixture of solutions is associative and closed, salt water would be the identity which is yielded from the mixture of the NaOH solution and HCl solution, assuming that all of the NaOH and HCl react to yield NaCl. The only reason I ask, is because mixing a solution with itself yields the same solution, and this is different from other groups like Z3. In the definition of a group I notice that the identity must hold for all elements and since this is not the case and the elements are not simply trivial copies of another, I would say there is only one identity. However, I am still hesitant to accept this example. Thanks for any input.