# Mike

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 Aug14 comment Convergent Subsequence in $\mathbb R$ Is it fair to say that since those subsequences are the only ones I have to consider because they are the only two convergent subsequences? Other than ones like $\langle a_{4k} \rangle$ which are contained within the one considered? Aug14 asked Convergent Subsequence in $\mathbb R$ Aug14 comment Proving that $\mu$ is $\sup S$ @JayeshBadwaik then why the $\Longleftrightarrow$? Aug14 comment Proving that $\mu$ is $\sup S$ Thank you. This is clear to me now @PeterTamaroff Aug14 accepted Proving that $\mu$ is $\sup S$ Aug14 revised Proving that $\mu$ is $\sup S$ redefined question Aug14 comment Proving that $\mu$ is $\sup S$ Ah! So Since we assumed that there is no $x \in [\mu -\epsilon, \mu]$ and arrived at $\mu \ne \sup S$ that means that $\mu$ is the supremum? Aug14 comment Proving that $\mu$ is $\sup S$ @BiditAcharya why does $\lambda \notin S \Longrightarrow \mu \ne \sup S$ Aug14 revised Proving that $\mu$ is $\sup S$ asked again Aug14 revised Proving that $\mu$ is $\sup S$ asked again Aug14 comment Proving that $\mu$ is $\sup S$ Ok I found my mistake there thank you @ArthurFischer Aug14 revised Proving that $\mu$ is $\sup S$ fixed mistake in forward direction Aug14 asked Proving that $\mu$ is $\sup S$ Aug14 comment Appropriate Notation: $\equiv$ versus $:=$ @AnonymousCoward see here: tex.stackexchange.com/questions/4216/how-to-typeset-correctly Aug14 revised Difference of two Cauchy Sequences edited body Aug13 revised Difference of two Cauchy Sequences added 16 characters in body Aug13 comment Difference of two Cauchy Sequences My mistake, I added the note that we are in $\mathbb R$ Aug13 revised Difference of two Cauchy Sequences added 16 characters in body Aug13 comment Are all infinities equal? I am interested by rigorizing "intuitive" statements such as "we can split these lines up and then 'add' them back together." For me, these are some of the hardest rigorous statements to make. How would you do it? Aug13 asked Difference of two Cauchy Sequences