Accumulation Points

An accumulation point (or limit point) of a set is a point where, no matter how closely you look, you can find other points of the set arbitrarily close to it. Essentially, it's a point that the set "approaches" repeatedly or densely around, even if the point itself isn't necessarily in the set. For example, in the set of all fractions between 0 and 1, the point 0.5 is an accumulation point because you can find fractions extremely close to 0.5. Accumulation points help describe the behavior and structure of sets in mathematics, particularly in analysis.