Memoryless System
A system is memoryless if for any $ t \in \mathbb{R} $ the output at $ t_0 \, $ depends only on the input at $ t_0 \, $(not past or future samples or informations).
System with Memory
A system is with memmory if for some $ t \in \mathbb{R} $ the output at $ t_0 \, $ doesn't only depend on the input at $ t_0 \, $, it also depends on past or future samples or informations.
