2Convergence of sequences

IA Analysis I



2 Convergence of sequences
Having defined real numbers, the first thing we will study is sequences. We
will want to study what it means for a sequence to converge. Intuitively, we
would like to say that 1
,
1
2
,
1
3
,
1
4
, ···
converges to 0, while 1
,
2
,
3
,
4
, ···
diverges.
However, the actual formal definition of convergence is rather hard to get right,
and historically there have been failed attempts that produced spurious results.

Contents