Set builder notation: is it ever used?

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Discussion Overview

The discussion revolves around the relevance and application of set builder notation in the context of physics and calculus. Participants explore whether it is essential to be familiar with this notation and its prevalence in mathematical literature.

Discussion Character

  • Conceptual clarification, Debate/contested, Homework-related

Main Points Raised

  • One participant questions the necessity of set builder notation in physics or calculus, expressing uncertainty about its usage.
  • Another participant asserts that set builder notation is fundamental and emphasizes the need to be comfortable with it.
  • A third participant echoes the sentiment of its importance but notes a lack of exposure to it in calculus textbooks.
  • A later reply challenges the previous claim about its absence in textbooks, suggesting that it is indeed present in more advanced mathematical texts, particularly those related to analysis and linear algebra.

Areas of Agreement / Disagreement

Participants express differing views on the importance and prevalence of set builder notation, with some asserting its necessity while others remain skeptical about its usage in their studies.

Contextual Notes

There is a lack of consensus on which mathematical texts adequately cover set builder notation, and participants reference different types of mathematics that may or may not include it.

JR Sauerland
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Should I sharpen up on using set builder notation? Like, will I ever need it in physics or calculus? I'm currently refreshing my skill at writing in Interval notation for inequalities and the like.
 
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I will go ahead and say that this is one of the very basic things one pretty much has to be perfectly comfortable with using and reading.
 
disregardthat said:
I will go ahead and say that this is one of the very basic things one pretty much has to be perfectly comfortable with using and reading.
I've just never seen it used anywhere. I've browsed through Calc books and never seen it :-S
 
I don't know what books you checked, but if you study a certain kind of math, it's only slightly less important than knowing the alphabet. Try a book with "analysis" in the title. (For example Friedman. I can assure you that even though the notation is only used a few times on the first few pages, you would use it all the time when you work through proofs and do problems). You should find it in any book on linear algebra as well. How else does the book define a subset before it asks you to determine if it's a subspace?
 
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