Memoryless System
A memoryless system is one that does not depend on certain parts of the function when its function gets scaled or time shifted in a certain direction. The only part of the function that matters is the x(t) part.
Example: in a function: $ x(t) = x(t)^2 + ((t-1)^2) $
the x(t) is the part of the function that will square the entire portion of the visible function, whereas the (t-1)^2 doesn't effect the output at all in the system.
System with Memory
A system that has memory is the same as above, with the addition of the extra time shift factor plays a part in the output of the function as well as the x(t) part of the function does.
Example: in a function $ x(t) = x(t)^2 + ((t-2)^2) $
a functions output can be shown by a squaring of the x(t) portion of the function, as well as a shift in the time by the ((t-2)^2) part.
