A community for students.
Here's the question you clicked on:
 0 viewing
2bornot2b
 3 years ago
Why is the approximation theorem of supremum called so? I mean why is it named "approximation theorem"?
2bornot2b
 3 years ago
Why is the approximation theorem of supremum called so? I mean why is it named "approximation theorem"?

This Question is Closed

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.3What result are you talking about?

2bornot2b
 3 years ago
Best ResponseYou've already chosen the best response.0I am talking about the following \[sup(a)\epsilon <x \le sup(a)\]

2bornot2b
 3 years ago
Best ResponseYou've already chosen the best response.0You know, I mean there exists an x etc etc

2bornot2b
 3 years ago
Best ResponseYou've already chosen the best response.0T.M Apostol calls is approximation theorem

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.3Give me the statement of the theorem. I don't know exactly what result you're talking about.

2bornot2b
 3 years ago
Best ResponseYou've already chosen the best response.0OK, I am stating it completely

2bornot2b
 3 years ago
Best ResponseYou've already chosen the best response.0Let S be a nonempty set of real numbers with a supremum, say b=supS. Then for every a<b there is some x in S such that \[a<x \le b\]

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.3Yes, ok. It's saying you can get arbitrarily close the the sup.

2bornot2b
 3 years ago
Best ResponseYou've already chosen the best response.0They call it the "approximation property of Reals"

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.3For example, let S be the set of all rational numbers < sqrt(2). The sup of that set is clearly sqrt(2). The result is saying in this case for any rational number less than sqrt(2), you can find another rational number close to sqrt(2) ... so you can approximate sqrt(2) better and better if you want to/need to.

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.3sure, if you ask nicely. And I'll nearly always ignore them if they're not fresh.

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.3in other words, if I find it when I log on, then I'm almost certain not going to respond.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.