Understanding Finite Dimensionality

[Schniz2]

Hi, i think i understand the definition of finite dimensionality.. however i am unsure of how to apply it to continuous and discrete time system expressions to determine whether or not they are finite or infinite dimensional systems. Is there a different way to think about the concept rather than the mathematical definition that if you can express it in the form of derivatives: [blah blah] for the continuous time case or the form [blah blah] for the discrete time case?

Dont know if what ive written makes any sense at all. I should have gone to bed hours ago :P.

Cheers