Basic basic set theory. Please help. Simple answer will suffice.

In summary, The person is encountering ellipsis in the use of a set and is confused about its meaning. They have been thinking about it for two hours and it is causing them distress. Ellipsis is used to indicate a continuation or omission in a sentence or set representation.
  • #1
andrewkg
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Hello my name is Andy I'm in high school, and I have a bit of a confusion or lack of information. Ok so I have been reading a book on set theory, and I keep encountering … ,but up more in the use of a set. Like A,B … but again up more to the middle of the sentence. I feel dumb, I googled it nothing, I've been thinking about it for around 2 hours. I cannot sleep it is bugging me so much. Thank you in advanced!
 
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  • #2
I keep encountering … ,but up more in the use of a set. Like A,B … but again up more to the middle of the sentence
You mean you keep encountering three dots like this "..." or "##\cdots##"?
They are called "ellipsis" and stand for the words "and so on", and mean that things continue as implied by what went before.

So:
##A,B,\cdots## means start going A B C etc and keep going in the same pattern ... so ##\{ 1,3,5,\cdots \}## would represent the set of positive odd numbers
##\{ 1,3,5,\cdots,27,29 \}## would be all the odd numbers from 1 through to 27 inclusive.
They are written like that because it would be boring to list every single member.

In a sentence it indicates, informally, a longish pause - in a quotation, it means that part of the quote that goes there was deleted for clarity.
At the end of a sentence it indicates that the sentence has been deliberately left unfinished.

See:
http://www.mathsisfun.com/sets/sets-introduction.html
http://en.wikipedia.org/wiki/Ellipsis
 

1. What is set theory?

Set theory is a branch of mathematics that deals with collections of objects, called sets. It provides a formal framework for describing and analyzing the relationships between these sets.

2. What are the basic concepts of set theory?

The basic concepts of set theory include sets, elements, subsets, unions, intersections, and complements. Sets are collections of objects, elements are the individual objects within a set, subsets are sets that are contained within another set, unions are the combination of two or more sets, intersections are the common elements between two or more sets, and complements are the elements that are not in a set.

3. What is the difference between a finite set and an infinite set?

A finite set is a set that contains a specific, countable number of elements, while an infinite set is a set that contains an uncountable number of elements. For example, the set of all integers is an infinite set, while the set of all months in a year is a finite set.

4. How are sets represented in set theory?

Sets can be represented in different ways, such as using braces { } to list the elements, using a roster method to list the elements, or using set-builder notation to define the elements based on a specific rule or condition.

5. How is set theory used in other fields of study?

Set theory is used in various fields of study, such as computer science, linguistics, and physics. In computer science, sets are used to represent data structures and in database management systems. In linguistics, sets are used to study the structure of language. In physics, sets are used to represent mathematical models and describe relationships between objects.

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