2bornot2b
  • 2bornot2b
Why is the approximation theorem of supremum called so? I mean why is it named "approximation theorem"?
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.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
JamesJ
  • JamesJ
What result are you talking about?
2bornot2b
  • 2bornot2b
I am talking about the following \[sup(a)-\epsilon
2bornot2b
  • 2bornot2b
You know, I mean there exists an x etc etc

Looking for something else?

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

More answers

2bornot2b
  • 2bornot2b
T.M Apostol calls is approximation theorem
JamesJ
  • JamesJ
Give me the statement of the theorem. I don't know exactly what result you're talking about.
2bornot2b
  • 2bornot2b
OK, I am stating it completely
2bornot2b
  • 2bornot2b
Let S be a nonempty set of real numbers with a supremum, say b=supS. Then for every a
JamesJ
  • JamesJ
Yes, ok. It's saying you can get arbitrarily close the the sup.
2bornot2b
  • 2bornot2b
They call it the "approximation property of Reals"
JamesJ
  • JamesJ
For 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
  • JamesJ
sure, if you ask nicely. And I'll nearly always ignore them if they're not fresh.
JamesJ
  • JamesJ
in other words, if I find it when I log on, then I'm almost certain not going to respond.
2bornot2b
  • 2bornot2b
OK, I understand.

Looking for something else?

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