Question #c66df

1 Answer
Alan P.
May 21, 2015

A function, #f(x)# is discontinuous at a point #x=hatx#
if

#f(hatx)# does not exist; but #f(hatx+-epsilon)# does exist for arbitrarily small values of #epsilon >0#

or

#lim_(hrarr0) f(hatx+-h) != f(hatx)#

Some simple examples:
#f(x) = 1/x# is discontinuous at #x=0# since the function is not defined at the at point

#f(x) = "Integer"(x)# is discontinuous since (for example)
#f(3-h) = 2 " for all " h>0#
but
#f(3) = 3#

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