So I’m trying to Self-teach myself on Vector Spaces and Dimensions and such. And I’m stuck on several aspects.
How are Vector Spaces used practically? I know they can be used to measure Scalars. But what kind of worth do “Scalars” have in the first place?
Is there a limit to how many Elements there can be in a Vector Spaces? Does it strictly have to be Finite or can there be a Countably or Uncountably Infinite amount? To my (very limited) knowledge, there can be both Infinite and Finite spaces. Especially when dealing with spaces that involve ℝ. Because, ya know all the real numbers are Uncountably Infinite in scope. Or can ℝ just represent finite values that happen to be Real Numbers?
When using the words “infinite Dimensional” what does this mean in a larger context? Is it literally an Infinite amount of Dimensions or is it just another way of just saying the space in question is Infinite?
Taking Baby Steps as you can prolly see.