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_{n}-x| is less than [itex]\in[/itex].

I also found a theorem that stated if a real sequence is bounded by a and b then it has an accumulation point c between a and b.

This confused me because if a sequence is bounded surely it is finite or at least could be finite in which case how does one find a value x such that there are INFINITELY many numbers in the sequence within [itex]\in[/itex] distance from it.

If somebody could explain conceptually how this is possible I would appreciate it.