Can vector space be infinite dimensional?

Not every vector space is given by the span of a finite number of vectors. Such a vector space is said to be of infinite dimension or infinite dimensional.

What does it mean to be higher-dimensional?

High Dimensional means that the number of dimensions are staggeringly high — so high that calculations become extremely difficult. With high dimensional data, the number of features can exceed the number of observations. For example, microarrays, which measure gene expression, can contain tens of hundreds of samples.

What does a higher dimension mean?

“It is just a space where you can go up-down, left-right, ahead-back, but also in one other dimension, something like leftB-rightB,” he says. “It is a bit like having many arms, like an Indian god.”

How do you think about infinity?

Five Ways to Think About Infinity

1. There isn’t one way to think about infinity.
2. Infinity isn’t any ordinary number.
3. There are infinite infinities.
4. The infinitely big and the infinitely small are infinitely related.
5. Forever and a day is different than forever.

What does infinite mean philosophy?

Aristotle and after It is always possible to think of a larger number: for the number of times a magnitude can be bisected is infinite. Hence the infinite is potential, never actual; the number of parts that can be taken always surpasses any assigned number.

Why can’t we understand Infinity?

For many of us, it’s easy to understand the concept of infinity, but we can’t comprehend how “big” or “never-ending” it is, because our perception of time always has a beginning and an end — minutes, days, years, lifespans.

What would life be like in a higher dimensional world?

Just one of the subtle economic effects of higher dimensional living. You’d also find that in 4 or more dimensions, you’d be able to do a lot of tricks impossible in 3 dimensions, like creating Klein bottles or (equivalently) taping the edges of two Möbius strips together. Sailing knots could take on stunning complexities.

What happens when you add more dimensions to the universe?

Physicist: Right off the bat, more dimensions means more freedom of movement. One of the more mundane effects of that is that in 4 dimensional space there’s an extra direction you can move and/or fall over in. So if you want to build a working bar stool you’d need at least 4 legs instead of just 3.

Can you imagine an infinite amount of Love?

It depends on what angle you’re looking at it from. You might be able to imagine an infinite love for your child or a lover because of what you feel inside, but thinking of the universe as having no boundaries and infinitely expanding is a different ball game. Is there anything beyond it?