LIMIT POINT Meaning and
Definition
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A limit point, also known as a cluster point or accumulation point, is a term used in mathematics to describe a point in a set that can be approached arbitrarily closely by other points of the set. More precisely, if we have a set S in a given metric space, a point p is said to be a limit point of S if for every positive real number ε, there exists a point q in S (other than p itself) such that q is within ε distance of p.
In simpler terms, a limit point is a point where the set "accumulates" around it, indicating that the set has elements that come arbitrarily close to that point. It does not necessarily mean that the point is included in the set, as it can be an external point too.
For example, let's consider the set S = {1, 1/2, 1/3, 1/4, ...}. In this set, the point 0 is a limit point because we can find elements of S (in this case, 1/n as n approaches infinity) that can get as close as we want to 0, even though 0 itself is not in the set S.
Limit points play a crucial role in topology, analysis, and other branches of mathematics where the concept of convergence or proximity is important. They help us understand the behavior and properties of sets, sequences, and functions, and provide a foundation for deeper mathematical investigations.
Common Misspellings for LIMIT POINT
- kimit point
- pimit point
- oimit point
- lumit point
- ljmit point
- lkmit point
- lomit point
- l9mit point
- l8mit point
- linit point
- likit point
- lijit point
- limut point
- limjt point
- limkt point
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- lim9t point
- lim8t point
- limir point
Etymology of LIMIT POINT
The word "limit point" is derived from the combination of two terms: "limit" and "point".
The term "limit" derives from the Latin word "limitis", meaning "boundary" or "extremity". It later entered English, retaining a similar meaning related to boundaries or the point at which something ends.
The term "point" also has Latin origins, originating from the Latin word "punctum", meaning "dot" or "point". It entered English in the 14th century, initially referring to a sharp end or tip.
In mathematics, the concept of a "limit point" refers to a point that is approached or approached by a sequence or set of points. The term was likely coined to describe this mathematical concept where a point is reached or limits the behavior of a sequence.
