My question is whether the systems below are memoryless or not:
$1.) \ y(t)=K$ where $K$ is a constant
$2.) \ y(t) = x(t_0) $ where $t_0$ is a constant
So, from the definition I have been using so far (A system is memoryless if its output at a given time is dependent only on the input at that same time), it seems like the first system is memoryless since the output at any time is fixed and can be said to depend only on the input at the same time.
For the second system, the output at $t=t_0$ depends only on $t_0$ but for any other time $t$, it requires knowledge of some other time i.e $t_0$ so I should classify it as having memory.
My doubt is if my reasoning is correct and if yes, isn't the second system a constant also which kind of confuses me.
I would really appreciate if someone could resolve this.