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Examples 3.3.2(a):

Take the sequence . Extract every other member, starting with the first. Then do the same, starting with the second.
The sequence in question is
= {-1, 1, -1, 1, -1, 1, ...}
If we extract every second number, starting with the first, we get:
{-1, -1, -1, -1, ...}
This subsequence now converges to -1.

If we extract every second number, starting with the second, we get:

{1, 1, 1, 1, 1, ...}
This subsequence now converges to 1.
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