anonymous
  • anonymous
What does the notation p:[0,1]-> Real mean?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
It means that p is a function from the closed interval [0,1] to the real numbers.
anonymous
  • anonymous
It means that p maps values from 0 to 1 to Real values.
anonymous
  • anonymous
Brilliant thanks! I'm guessing that means any number between 0 and 1 which isn't necessarily an integer? (sorry if that sounds obvious)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Yes, any real number in that interval.
anonymous
  • anonymous
So, uhm, the rest actual question asks you to show that the set \[\Pi _{n}=\left\{ p:[0,1]\rightarrow \mathbb{R} | \sum_{n}^{j=0} a _{j}x ^{j}, a _{0},...,a_{n} \in \mathbb{R}\right\}\] equipped with pointwise addition and scalar multiplication is a vector space, by verifying the 8 axioms of vector spaces. Oh and \[n \in \mathbb{N}\] So with the associativity of addition axiom, I would need to show: \[p(x),q(x),r(x) \in \Pi_n, (p+(q+r))(x) = ((p+q)+r)(x)\] (Correct me if I'm wrong) Would I do this by say that by pointwise addition and because p,q,r(x) in Real, (in which associative addition holds) \[(p+(q+r))(x) = p(x)+(q(x)+r(x)) = p(x)+q(x)+r(x) = (p(x)+q(x))+r(x) = ((p+q)+r)(x)\] I can't seem to get my head round this sort of maths. I never know how rigorous the proofs have to be either...
anonymous
  • anonymous
This displays messily in chrome but shows the whole line, in Firefox the end of the line is missing so I'll post again... and I made a pigs ear of the sentence above it :") Would I do this by saying that, due to pointwise addition, and because p(x),q(x) and r(x) are real numbers (hence addition of p,q,r is associative) \[(p+(q+r))(x) = p(x)+(q(x)+r(x)) = p(x)+q(x)+r(x)\]\[ = (p(x)+q(x))+r(x) = ((p+q)+r)(x)\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.