Is the set of all continuous functions on the interval [0,1] a vector space?

In summary: And I am almost 30, so high school was... a while ago...In summary, the conversation discusses the properties of a vector space and applies them to the set of continuous functions on the interval [0,1]. The conversation then moves on to discussing the set of non-negative functions and the differences between continuous and non-continuous functions in a vector space. The speaker also mentions their lack of prior knowledge in math due to dropping out of high school, but is determined to learn linear algebra.
  • #36
Anyone else want to chime in? This is all new to me:rolleyes:

You can't just say that a+b is polynomial of degree n with zero coefficients?

But like I said, this is new to me. :smile:
 
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  • #37
Saladsamurai said:
Anyone else want to chime in? This is all new to me:rolleyes:

You can't just say that a+b is polynomial of degree n with zero coefficients?

But like I said, this is new to me. :smile:

nicksauce makes a good point. The question does say "degree EXACTLY n". The 'exactly' is likely there for a reason.
 
  • #38
Okee-dokee. So since there is some polynomial of degree exactly n that when added to some other polynomial of exactly degree n does not YIELD a polynomial of exactly degree n, then the set of all polynomials of exactly degree n IS NOT a vector space.

So my coefficients of zero thing in post #36 is valid.
 
  • #39
Right. You could also think of cases like p=x^2 and q=x^2-x, so p-q=x. Not a polynomial of degree EXACTLY two. If they had said polynomial of degree two or less, then it would be a vector space.
 
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