Unfamiliar Notation: \bigcup & \bigcap Explained

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In summary, the symbols \bigcup and \bigcap are used in mathematics to represent set operations. \bigcup represents the union of two or more sets, while \bigcap represents the intersection of two or more sets. These symbols are read as "union" and "intersection" and are pronounced as "cup" and "cap" respectively. They are used to combine or compare sets in order to find common elements (using \bigcap) or elements in either set (using \bigcup). Other symbols related to \bigcup and \bigcap in set theory include \subseteq, \supseteq, and \setminus. These symbols can be used with any number of sets, allowing for operations on multiple sets at once
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Lank
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Homework Statement



Having trouble recognizing this notation.
Let Ai = {i, i + 1, i + 2, . . . } for i = 1, 2, . . . . What
are:


[tex]\bigcup[/tex] A (subscript i)
i=1

and


[tex]\bigcap[/tex] A (subscript i)
i=1

Homework Equations


I know what the [tex]\bigcup[/tex] or [tex]\bigcap[/tex] notation means in sets and subsets, but not in sequences and summations.

The Attempt at a Solution



I don't need it explained, I simply need to know what the [tex]\bigcup[/tex] and [tex]\bigcap[/tex] stands for so I can read up on them. Thanks guys. I can also upload the pdf attachment if needed.
 
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  • #2
[tex]\bigcup[/tex] - union - A1 U A2 U ... U An
[tex]\bigcap[/tex] - intersection - same as above but with the intersection symbol
 
  • #3
Thanks.
 

1. What is the meaning of the symbols \bigcup and \bigcap?

The symbols \bigcup and \bigcap are used in mathematics to represent set operations. \bigcup represents the union of two or more sets, while \bigcap represents the intersection of two or more sets.

2. How do you read and pronounce the symbols \bigcup and \bigcap?

The symbol \bigcup is read as "union" and pronounced as "cup", while \bigcap is read as "intersection" and pronounced as "cap".

3. How do you use \bigcup and \bigcap to solve problems?

\bigcup and \bigcap are used to combine or compare sets in order to find the elements that are common to both sets (using \bigcap) or the elements that are in either set (using \bigcup). These symbols are often used in set theory, probability, and statistics.

4. Are there any other symbols that are related to \bigcup and \bigcap?

Yes, there are other symbols that are related to \bigcup and \bigcap in set theory. Some examples include \subseteq (subset), \supseteq (superset), and \setminus (set difference).

5. Can \bigcup and \bigcap be used with more than two sets?

Yes, \bigcup and \bigcap can be used with any number of sets. For example, if we have three sets A, B, and C, then A \bigcup B \bigcup C represents the union of all three sets, and A \bigcap B \bigcap C represents the intersection of all three sets.

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