Set builder notation: is it ever used?

In summary, understanding and being comfortable with using set builder notation is a fundamental skill in mathematics, particularly in subjects such as analysis and linear algebra. While it may not be used frequently, it is essential for working through proofs and solving problems. This notation can be found in books with "analysis" in the title, as well as in linear algebra textbooks.
  • #1
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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  • #2
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.
 
  • #3
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
 
  • #4
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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1. What is set builder notation?

Set builder notation is a method used in mathematics to describe a set of numbers or elements. It is written in the form {x | x is a member of a set and satisfies a certain condition}.

2. When is set builder notation used?

Set builder notation is used when describing sets that have a specific pattern or property. It is commonly used in algebra, calculus, and other branches of mathematics.

3. Can set builder notation be used for infinite sets?

Yes, set builder notation can be used for infinite sets. For example, the set of all positive even numbers can be written as {2n | n is a positive integer}.

4. What are the advantages of using set builder notation?

Set builder notation allows for a concise and clear representation of a set, making it easier to work with in mathematical expressions and equations. It also allows for the description of infinite sets.

5. Are there any limitations to using set builder notation?

One limitation of set builder notation is that it may not be suitable for describing sets with complex or non-mathematical properties. In these cases, other methods such as roster notation may be more appropriate.

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