#lim_(xrarra)f(x)# does not exist

The idea is that there is no number that #f(x)# gets arbitrarily close to for #x# sufficiently close to #a#.

For a function #f# defined in some open interval that contains #a#, except possibly at #a#,

#lim_(xrarra)f(x)# does not exist if and only if

there is no number #L# such that for every #epsilon > 0#, there is a #delta > 0# with: for all #x#, if #0 < abs(x-a) < delta#, then #abs(f(x)-L) < epsilon#

equivalently

for every #L# there is some #epsilon > 0# such that for every #delta > 0# there is some #x# with #0 < abs(x-a) < delta#, and #abs(f(x)-L) >= epsilon#