Register to reply

Why why why (tiny limsup proof)

by quasar987
Tags: limsup, proof, tiny
Share this thread:
quasar987
#1
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 Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
Dick
#2
May13-07, 03:10 PM
Sci Advisor
HW Helper
Thanks
P: 25,228
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