Comments
The exmple you give should be a system with memory, as the output also depends on input at$ t = 4\, $ or$ x(4)\, $. Since it depends on the future input, its a system with memory. - Wei Jian Chan
Your definition is spot on but I would've liked an example for both a memoryless system and a system with memory. - Max Paganini
While your definition is a really good way to reword what was given in class, your example is in fact a system with memory and not a memoryless system. It depends on $ x(2) $ and $ x(4) $, so it would depend on $ x(t+2) $, making 2 your $ k $ integer.
