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# Sup, Inf, Lim Inf/Sup Watch

1. Right, so I need a solid picture of what these look like.
I know the definitions, can someone give me some sort of picture of what the lim{sup{x}n} looks like (and respectively inf)

I haven't really got a solid picture in my head.
Also, can we no just treat the points of sup and inf of a sequence as a subsequence, of the the original Real sequence?

Best Wishes,

Daniel Williams
2. anyone?
Right, so I need a solid picture of what these look like.
I know the definitions, can someone give me some sort of picture of what the lim{sup{x}n} looks like (and respectively inf)

I haven't really got a solid picture in my head.
Also, can we no just treat the points of sup and inf of a sequence as a subsequence, of the the original Real sequence?

Best Wishes,

Daniel Williams
I'm guessing (your notation isn't very clear) that you mean limsup(x^n) where x is a constant real.

You're going to have to divide this into the cases:
x>1, x=1, -1<x<1, x= -1, x< -1

As an example:

limsup((-1)^n) = 1 and liminf((-1)^n) = -1.

Also, if (a_n) converges, then

limsup(a_n) = liminf(a_n) = lim(a_n)

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Updated: December 9, 2010
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