:: deftheorem defines convergent_in-infty LIMFUNC1:def 9 :
for f being PartFunc of REAL,REAL holds
( f is convergent_in-infty iff ( ( for r being Real ex g being Real st
( g < r & g in dom f ) ) & ex g being Real st
for seq being Real_Sequence st seq is divergent_to-infty & rng seq c= dom f holds
( f /* seq is convergent & lim (f /* seq) = g ) ) );