Register to reply

Why why why (tiny limsup proof)

by quasar987
Tags: limsup, proof, tiny
Share this thread:
May11-07, 09:59 PM
Sci Advisor
HW Helper
PF Gold
quasar987's Avatar
P: 4,771
There's a "theorem" in my book that says if x is a cluster point of {x_n}, then lim inf(x_n)[itex]\leq[/itex]x[itex]\leq[/itex]lim sup(x_n).

The way the author proves it is a little bit extravagant. Why not just say "Let A be the set of all cluster points. Then, lim inf(x_n)=inf(A)[itex]\leq[/itex]x[itex]\leq[/itex]sup(A)=lim sup(x_n)."

Phys.Org News Partner Science news on
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
May13-07, 03:10 PM
Sci Advisor
HW Helper
P: 25,243
Don't they pretty much say the same thing?

Register to reply

Related Discussions
Limsup h.w. proofs Calculus & Beyond Homework 1
Limsup and liminf Calculus 13
Analysis..limsup(inf) |sinn|^1/n = ? it`s not easy.. Calculus 7
Help with liminf and limsup Calculus & Beyond Homework 1
Another limsup and lim inf question Calculus 2