Let #a# is real number and #epsilon>0#. Defined that #V_epsilon(a)={x:|x-a|<"epsilon}#. If #a!=b#, how to determine #epsilon>0# and #delta>0# so that #V_epsilon(a)nnV_delta(b)=O/# ?

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#a#
#epsilon>0#
#V_epsilon(a)={x:|x-a|<"epsilon}#
#a!=b#
#epsilon>0#
#delta>0#
#V_epsilon(a) nn V_delta(b)=O/#

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Answer 1 · 2017-12-17T13:50:50

Make the sum #epsilon + delta # less than or equal to the distance between #a# and #b#, which is #abs(a-b)#