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limit point
This term is a technical expression used exclusively within the fields of mathematical analysis and topology. It describes a point of accumulation where elements of a set cluster infinitely close, regardless of whether the point itself belongs to that set.
In a pedagogical context, it is often contrasted with an isolated point, which has a neighborhood containing no other points of the set. Because it is a compound noun referring to a specific mathematical entity, it follows standard English pluralization rules.
Meanings
Examples
The set of rational numbers has every real number as a limit point.
Is this point actually a limit point or just an isolated point?
I need to prove that x is a limit point of the sequence.
Every neighborhood of the limit point must contain another element of the set.
The professor explained how to identify a limit point in a metric space.
Wait, if the set is finite, it cannot have a limit point.
The derived set consists of all the limit points of the original set.
I wonder if this specific value functions as a limit point for the function's range.