Cauchy's definition of a limit | YegerMaster

The limit of a Sequence is defined by Cauchy
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A third video goes even deeper into this definition

[@bernatboschfolch]

Is the cauchy definition only valid for definition of the limit when a sequence goes to infinitum? Can we use the same definition to find the limit as the sequence defined by 1/|n| approaches to n=0 ? Should then epsilon be a distance created in the x axis in the suroundings of the value x=0 to create a vertical zone of aproximation to x=0 instead of an horizontal range to create an horizontal zone of aproximation to y=0 as in this case when we observe the limit of the function as it goes to infinitum?

[@YegerMaster]

Hi Bernat! In Cauchy's definition Epsilon epsilon always represents the distance on the y-axis. We can still approach x=0 for example, and not necessarily with the sequence 1/n, but with a lot of different sequences. Yet, either way epsilon is still on the y-axis.