Talk:Real Analysis/Sequences

A minor problem with 'Algebraic Operations on Sequences'

I believe that there is a problem with the 4th result (about quotient of 2 limits) I reckon it is not enough that y_n is non-zero for all n, but believe that we also need to assume that the limit of the y's is also nonzero. Otherwise there would exist a counter-example where the y_n are alternatively positive and negative, while tending to zero.

Does anyone agree?

82.27.163.136 10:07, 18 February 2006 (UTC)madmath789

Yes, your correct, and now the article assumes the limit is not zero, but allows some of the y_n's to be zero. Thenub314 (talk) 15:41, 5 January 2009 (UTC)

Completeness
There seems to be a general confusion here about the differences between the least upper bound property and completeness. In particular some of the theorems stated are not equivalent to the least upper bound axiom, and hence could not be used as an axiom defining the real numbers. I think we should be a bit more careful about how we use the term completeness. Thenub314 (talk) 15:45, 5 January 2009 (UTC)

limit superior
How this definition define limit superior and for what kind of sequence we can define limit superior? Anuvabd1 (discuss • contribs) 06:03, 7 May 2019 (UTC)