It's like this.
I didn't have any problems to prove some of definitions of sequences like :
for any . Starting from some index every member of sequence are in -region of point x. Same, from some index every member of sequence are in -region of point y.
If we put then for every these inequality are true :
so from inequality of triangle for we have:
Because is fix real number and any small number so it's any small number so there we have that is:
This and some another I got it OK
But I can't, or don't see how to prove (or show) that sum of two null-sequences are again null-sequence (and difference of two sequences) becose it's to obviously. And for the product of two null-sequences is null-sequence and how we can relax conditions for the product of two null-sequences?
any help will be most appreciated
Thanks very much