Zulip Chat Archive

Stream: Is there code for X?

Topic: Sup and Inf in R have sequences converging to them


view this post on Zulip Keefer Rowan (May 28 2020 at 17:45):

Is there theorem of the form ER,E bounded and nonempty {an}E,ansupE\forall E \subseteq \mathbb{R}, E \text{ bounded and nonempty } \to \exists \{a_n\} \subseteq E, a_n \longrightarrow \sup E?

view this post on Zulip Kevin Buzzard (May 28 2020 at 22:30):

So we certainly have that E has a sup, but you might have to build the sequence by hand unless there's some trick with filters :-)

view this post on Zulip Yury G. Kudryashov (May 29 2020 at 05:12):

Do you want this sequence to be increasing?


Last updated: May 16 2021 at 05:21 UTC