Problem 1.1.A basket of fruit is arranged out of apples, bananas, and oranges.What is the smallest number of fruit that should b
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Let be a sequence that converges to
. This means for any
, there is some
such that
for all
. From this inequality we see that
, so it follows that
.
On the other hand, let be a sequence that converges to 0. This means
for all large enough
, and we get the simpler inequality for free,
, so it follows that
.