Structured with task, recycled earlier from earlier, to make sure that the tasks do not get counted as Runestone reading activities (since they are inside an <exercise> inside of an <exercises> division.
The vector space of all polynomials with finite degree has a basis, , which is infinte.
False.
The vector space of all polynomials with finite degree has a basis, , which is infinte.
Hint.
, the vector space of polynomials with degree at most , has dimension by Theorem 3.2.16. [Cross-reference is just a demo, content is not relevant.] What happens if we relax the defintion and remove the parameter ?