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    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
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    anyone?
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    pretty please?
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    (Original post by HyperNGifted)
    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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