Question

I have a stupid question regarding vectors spaces

Answer 1

Now that you are familiar with vector spaces, try determining if other sets of objects meet the requirements (or not). For example, the set of integers, the set of rationals, the set of positive continuous functions on a closed interval. Do these meet the definition of a vector space? If not, why? Can you think of other examples from your past?

Answer 2

Not a stupid question. Are the integers over the integers a vector space?

Answer 3

ummm i dont think so

Answer 4

on this one, note that you must have a field as the basic algebraic structure. The integers are not a field. Hence the integers over the integers are not a vector space.

What about the rational numbers over the rationals?

Answer 5

lol ya it does

Answer 6

that was a wild guess

Answer 7

yes, the rationals are a field.

Answer 8

y is that so?

Answer 9

Fields is a set together with two operations: addition + and multiplication x, which satisfies just about every axiom of the real numbers. Such as there exists a number 0 such that
0 + x = x for all x.

The rationals behave in the right way.

Anyway, let's stick with the real numbers. The finite polynomials are a vector space over the reals also.

Answer 10

If you go hunting on the internet, you'll find lots and lots of examples.

Answer 11

yes oook i get it now :D

Answer 12

Just needed a lil bit of coaching Thanks :D

Answer 13

Great work both of you!

Answer 14

awwww Thanks shalvey

Answer 15

Os is a savior I really like it =)