Have you ever made a book which consists of a collection of the posts from this blog? If not, is there any way to download all your posts on this blog?

Thanks!

Peter Yang

*[All books published from 2008 onward were initially posts on this blog. -T.]*

i have a general question.is mathematics something that which already exists in nature and you people are discovering it or is it an invented concept….

]]>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.

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