The span of an infinite set is the set of all possible linear combinations of the elements in the set. In other words, it is the set of all possible combinations of the vectors in the set.
A finite set has a limited number of elements, and therefore a limited number of possible linear combinations. In contrast, an infinite set has an infinite number of elements and an infinite number of possible linear combinations.
The span of an infinite set is important because it allows us to understand the properties and relationships of the elements in the set. It also helps us to solve complex mathematical problems and prove theorems.
Yes, the span of an infinite set can be visualized as a vector space in which the elements of the set are represented by vectors. The span is then the set of all possible linear combinations of these vectors, which can be visualized as a geometric shape in the vector space.
The span of an infinite set can be calculated by finding a basis for the set, which is a set of linearly independent vectors that can be used to represent all other vectors in the set. The span is then the set of all possible linear combinations of the basis vectors.