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Bob

]]>Construct a sequence with elements in S such that all terms are different. This should be possible because S is infinite. Now, because this sequence is bounded, it must have a convergent subsequence which is non-constant.

Hence, it follows that S' is non-empty.

]]>Does "Pseudo Compact" in this case the same as "Anti-Compact" ? Then how can we describe the "Pseudo-Compact" subsets of Real Numbers?

]]>How about too easy. That will take care of tary-try-tree-tri-trey.

]]>NOTE: These exercises refer to the material posted in

thisthread.#1

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This is a test question from the CBSE.

This question may violate copyright. All future answers may be deleted.

How to use a forum:

All forums are there to converse and answer questions. It is a great opportunity to get help. But all forum members are under an obligation to do the right thing. To cause no harm.

Lao Tsu wrote:

If you give a hungry man a fish, you feed him for a day, but if you teach him how to fish, you feed him for a lifetime. - old Sicilian saying

Most forum members will not answer homework or test questions. I will under certain conditions, if the questioner shows that he has tried and failed many times, I will give the answer if I can. This process of trying and failing is extremely important. It teaches perseverance and the right type of thinking. Dealing with failure is mandatory, since we will fail every day that we live.

I can give you the equation of the circle in terms of c. It is a bit involved and long. But I can not try to help unless I know where you need help. So, what have you tried to solve this? Let me see what you think.

Loopholes: There are always ways out of any predicament and no one knows that better than me... You posted this in Exercises, all of the above comments are basically for Help Me! If you know the answer and are posing this as a problem for others to solve then I will just blurt out the answer before anyone else does. I was the fastest in class, at work and just about anywhere else. True, I ain't 25 anymore but at 96 and toothless I will still take on any whippersnapper in a forum and on the trail.

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How would you use this information to construct an arbitrary number of limit points?

]]>I am sorry if you have been offended. I had every reason to believe you were pulling my leg.You only had given me the value of x=3 ,not chosen by me.

In addition taking dx=0.02 does not confirm to its being infinitesimal. So that may not be what is expected.]]>

Bob

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