aumenta hasta llegar a una asíntota para n=∞

20:09 May 19, 2011 

The literal translation of the given sentence is
"On incrementing n, AT*n cycles(a) increases, reaching an asymptote when n= ∞." n is the number of cycles (of the irradiation trial, its values are n=1, 2, 3, ...) but it's not clear what AT*n cycles(a) is - some sort of function of n, call it f(n) to use standard notation.

The above may be the best way to translate the sentence, but it's mathematically sloppy and should be written as something like

"f(n) is a monotonically increasing function of n which tends towards (value of asymptote) as n=1, 2, 3, ... tends to infinity."

"n = ∞" should really not be written in this context.

16:09 May 19, 2011 

I don't think so Phil. If you look at the second diagram in http://en.wikipedia.org/wiki/Hyperbola
you'll see the curve asyptotically approaching a straight line as the variable increases. That's the sort of thing that's meant here.

16:05 May 19, 2011 

I'm not a mathematician, but could this just mean "increases asymptotically to infinity"?