Property 5: Memoryless.
In my understanding, if a function has "memory", the output y(t) (or y[n]) depends not only on the current input value, but also depends on the previous input values. It reminds me the state machines in EE270 class. One of them is call "mealy" and depends on both states and input, another one called "moore" depends only on states. That's kinda the same way as the functions property: memoryless.
Examples of memoryless functions: y[n] = k*x[n]+c y(t) = k*x(t)+c h[n] = 0 for all n != 0 h(t) = 0 for all t != 0
Examples of not memoryless functions: y[n] = k*x[n-n0] +c y(t) = k*x(t-t0) +c h[n] != 0 for all n!=0 h(t) != 0 for all t!=0
