Unfamiliar Notation: \bigcup & \bigcap Explained

  • Thread starter Thread starter Lank
  • Start date Start date
  • Tags Tags
    Notation
AI Thread Summary
The discussion focuses on the notation \bigcup and \bigcap in the context of sequences and summations. The user seeks clarification on the meaning of these symbols, specifically in relation to the sets defined as Ai = {i, i + 1, i + 2, ...} for i = 1, 2, ... The \bigcup notation represents the union of all sets Ai, resulting in the set of all natural numbers. Conversely, the \bigcap notation denotes the intersection of all sets Ai, which is empty since there is no common element across all sets. Understanding these notations is crucial for interpreting set operations in mathematical contexts.
Lank
Messages
6
Reaction score
0

Homework Statement



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


\bigcup A (subscript i)
i=1

and


\bigcap A (subscript i)
i=1

Homework Equations


I know what the \bigcup or \bigcap 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 \bigcup and \bigcap stands for so I can read up on them. Thanks guys. I can also upload the pdf attachment if needed.
 
Last edited:
Physics news on Phys.org
\bigcup - union - A1 U A2 U ... U An
\bigcap - intersection - same as above but with the intersection symbol
 
Thanks.
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
Back
Top