- #1
Awatarn
- 25
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How could I proof that [tex]F^\int[/tex] is infinite vector space?
An infinite vector space is a mathematical concept that describes a collection of vectors that can be added and scaled infinitely. In other words, there is no limit to the number of vectors that can exist in this space.
A finite vector space has a limited number of vectors, while an infinite vector space has an infinite number of vectors. Additionally, a finite vector space has a finite dimension, while an infinite vector space has an infinite dimension.
Some examples of infinite vector spaces include the space of all polynomials, the space of all continuous functions, and the space of all sequences.
No, an infinite vector space cannot have a finite basis. This is because a basis is a set of linearly independent vectors that can be used to span the entire vector space. In an infinite vector space, there is no finite set of vectors that can span the entire space.
Infinite vector spaces are used in various fields of science, including physics, engineering, and computer science. They are used to model continuous phenomena and to solve complex problems that involve infinite dimensions, such as optimization and data analysis.