Why why why (tiny limsup proof)


by quasar987
Tags: limsup, proof, tiny
quasar987
quasar987 is offline
#1
May11-07, 09:59 PM
Sci Advisor
HW Helper
PF Gold
quasar987's Avatar
P: 4,768
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
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered
Dick
Dick is offline
#2
May13-07, 03:10 PM
Sci Advisor
HW Helper
Thanks
P: 25,165
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