Question

What is a supreme limit?

Answer 1

a limit which is supreme?

Answer 2

sry

Answer 3

supreme sub

Answer 4

supreme sub ... havent come across that term yet.

if im reading this right, limsup is the upper bound; and liminf is the lower bound, of a series or sequence

Answer 5

a sup is the lowest upper bound .... hmmm

Answer 6

sup or sub?

Answer 7

lagrange wrote sub u wrote sup

Answer 8

sup is shorthand for supreme

sub might mean lower, or be a typo :)

Answer 9

sometimes i can read the technical jargon, but for the most part its like greek to me :)

Answer 10

\[\limsup_{n\to\infty}\,x_n = \lim_{n\to\infty}\left(\sup_{m\geq n}x_m\right)\]
\[\liminf_{n\to\infty}\,x_n = \lim_{n\to\infty}\left(\inf_{m\geq n}x_m\right)\]

For example...if \(x_n=(-1)^n\) then

\[\limsup_{n\to\infty}\,x_n=1\] and \[\liminf_{n\to\infty}\,x_n=-1\]