Zulip Chat Archive

Stream: general

Topic: limit of a series of sets


view this post on Zulip Simon Hudon (Apr 06 2018 at 05:03):

I have an infinite series of sets that each include their successor and such that each is non-empty. How do I prove that the intersection of all sets is also non-empty?

variables
   (s : stream (set α))
   (h₀ :  i, s i  )
   (h₁ :  i, s (i+1)  s i)
example : ( i, s i)   := ...

view this post on Zulip Mario Carneiro (Apr 06 2018 at 05:46):

it's false? For example take s n := {m : nat // n <= m}

view this post on Zulip Kenny Lau (Apr 06 2018 at 05:47):

right, it’s false

view this post on Zulip Kenny Lau (Apr 06 2018 at 05:47):

i was thinking for 5 minutes whether it is true or false

view this post on Zulip Kenny Lau (Apr 06 2018 at 05:47):

take (0,1/n)

view this post on Zulip Simon Hudon (Apr 06 2018 at 11:34):

Damn it! You guys are right! I was hoping to generalize a theorem. I guess I'll have to keep thinking about restrictions

view this post on Zulip Chris Hughes (Apr 06 2018 at 13:37):

(deleted)


Last updated: May 08 2021 at 04:14 UTC