Coterminal & subsequences

Given a sequence (or more generally, net),
a limit for the net -> limit for all -coterminal- (!) subnets.

[For sequences, any (necessarily infinite!) subsequence is coterminal,
 but for general nets you can get "stuck":
 maybe you have a finite subset, or maybe you have infinitely many elements that don't "go to the end": EG, f(x) = x for x<1, 0 for x geq 1;
 this has a limit as you go to infinite, but not on the subnet that
 consists of x<1 ]

Conversely, -if the net is monotone- (order preserving),
then a limit for a coterminal subnet implies a limit for the whole net.

However, if it's not monotone, you can't so conclude.
[Obviously a divergent coterminal subnet implies that the whole diverges.]

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This is just formality for the usual "subsequences converge"
