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Limiting Process

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Generally speaking, a limiting process is a theoretical “ceiling” or “floor” that prevents whatever is underneath (anything from numbers to functions to subatomic particles) from moving past a certain point.

Types of Limiting Process

limit points boundary points example

A limiting process for a shape prevents points 4 and 5 from entering the process.



In mathematics, there are several types of limiting process. The term can refer to the general process of finding limits of functions or finding derivatives using a limiting process. But it can also refer to a specific process such as:

  • The xi-limiting process, used in particle physics to study bosons [1],
  • A geometric limit. For example, the limit of a chord as it approaches a tangent, or the early process used by mathematicians to approximate the area of a circle.
  • A discrete process, such as:

In a broader sense, these processes can lead to an understanding of different types of infinity. The limiting process tends to suggest that infinity is unattainable, but further study of the rate of approach to infinity can suggest other, attainable, types of infinity [2].


Other Types of Limiting Process

Interestingly, even wars can have limiting processes, which depend on “appreciation of the pressures which affect policy makers in making decisions related to limiting war”. For example, two sides probably desire to avoid thermonuclear destruction, staying under that ceiling and preventing war from becoming total [3].

In biology, self-limiting means an organism (or colony of organisms) that is limited in growth. A self-limiting disease (like the common cold) that resolves naturally without treatment [4]. Any organism is going to have that artificial celling that prevents further growth, whether it’s genetics, environmental conditions (like human antibodies), or death of the host [5].

References

[1] Lee, T. (1962). Application of Xi-Limiting process to intermediate bosons. Retrieved April 19, 2021 from: https://www.osti.gov/biblio/4776925
[2] Tall, D. Mathematical Intuition, with Special Reference to Limiting Processes. Retrieved April 19, 2021 from: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.377.5692&rep=rep1&type=pdf
[3]. Halperin, Morton. (1961). The Limiting Process. Retrieved April 19, 2021 from: https://findit.library.yale.edu/catalog/digcoll:567083
[4] Bickle, I. & Bell, D. Self-Limiting. Retrieved April 19, 2021 from: https://radiopaedia.org/articles/self-limiting-2?lang=us#:~:text=Self%2Dlimiting%20(a.k.a.%20self%2D,taking%20any%20form%20of%20medicine.
[5] Kane, M. & Golovkina, T. Common Threads in Persistent Viral Infections. Retrieved April 19, 2021 from: https://jvi.asm.org/content/84/9/4116


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Stephanie Glen. "Limiting Process" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/limiting-process/
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