In Analysis I, Definition 6.4.1, a limit point is continually ε-adherent to the sequence mentioned for every ε>0.

Then using the observation under the remark 5.4.11, that the preposition 4.3.7 holds for reals, from 4.3.7 (a) and Definition 6.4.1 can we conclude that there exists a N >= m for which each n >= N the limit point is always equal to each member of the sequence for n>= N?

(In high school we were told that the sequence approaches infinitely the limit point but never “touch” it).

Thanks in advance.

(Undergraduate student) ]]>

*[Which book are you referring to? – T.]*

*[One can use some portion of the factor to eliminate if is large enough. (One could also eliminate the factor in this fashion, if desired.) -T.]*

Exercise 2.2.2.

Lemma 2.2.10. Let “a” be a positive number. Then there

exists exactly one natural number b such that b++ = a.

I am an autodidact person , but i can’t solve this exercise. please help.

]]>My name is Ishreet and I study in Sydney in Australia.I am in grade 3.Do you have any grade 3 books for me?Can you please advice?

Thanks

]]>I find it amazing that you have written all these books considering you are a Fields Medalist and do so much research. How do you complete the books without it interfering with your research? Or is it just that you don’t see yourself as being on the clock to produce your life’s work? I noticed some of these were produced before you got the award, so it doesn’t seem like a “going soft”. Do you feel these projects have somehow helped your research?

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