When dealing with isolated singularities, we classify each of these points as removable, pole (of order $k$), or essential. It easy to see that all isolated singularities must be of one of these three categories by construction:

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> > We define any isolated singularity that isn't removable or pole as an *essential singularity*.
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Why is it that we throw all other singularities into this category? Do we not care about essential singularities to classify them further? That is, are removable singularities and poles (of order $k$) the only isolated singularities we care about?