Question

Suppose \(\{x_n\}_n \ , \ \{y_n\}_n \subset R\), show that
\(\limsup x_n + \liminf y_n \le \limsup(x_n+y_n)\)

Answer 1

to hard for my brain

Answer 2

suppose x_n, y_n are in R
show that
lim sup x_n + lim inf y_n <= lim sup (x_n+y_n)

Answer 3

latex isn't working... it went on vacation

Answer 4

thats why i rewrote it:)

Answer 5

still stuck on my question D:

Answer 6

I thought callisto helped you with it

Answer 7

yeah, but some parts I just don't get it... unless I just use the laws or something

Answer 8

@UsukiDoll @ganeshie8

Answer 9

latex is broken on here.

Answer 10

@eliassaab how is this
limsup(x_n) = limsup(x_n+y_n-y_n)<=limsup(x_n+y_n)+limsup(-y_n) =
limsup(x_n+y_n)-liminf(y_n)
so the result follows.