You're definitions are very good, except a system is considered to have memory when its current output is dependent on future values of the input and output also. - Christen Juzeszyn
Correct, clear to me. - Ronny Wijaya
These definitions are both correct and simple to understand. I might change the wording "It doesn't take in..." to say, "It doesn't depend on...", but this is simply a matter of personal preference to wording then anything that is really incorrect. As mentioned above, you did forget to mention that a system with memory depends on the future as well as the past.
