# Thread: Hey guys! What operation is this symbol?

1. ## Hey guys! What operation is this symbol?

Hey guys. To introduce myself to the forum, I'm a first (going on second) year Computer Science student from Liverpool UK. Just a quick question on a symbol I have come across;

I know the union of sets, $\displaystyle A \cup B$ joins all elements in A and B. As far as I can tell from the description it is the union of all the sets $\displaystyle$A_{x}$$where \displaystyle x is an element of \displaystyle X. The lines being the cardinality of this set which has been joined (union). Am I close at all to it's meaning? If so, could you then have a big intersect symbol to intersect the sets produced. There is also an example later with \displaystyle b \in C under the big union symbol, is this just a condition for the union operation? Thanks guys Phil 2. ## Re: Hey guys! What operation is this symbol? Originally Posted by philleonard Hey guys. To introduce myself to the forum, I'm a first (going on second) year Computer Science student from Liverpool UK. Just a quick question on a symbol I have come across; I know the union of sets, \displaystyle A \cup B joins all elements in A and B. As far as I can tell from the description it is the union of all the sets \displaystyle A_{x}$$ where $\displaystyle x$ is an element of $\displaystyle X$. The lines being the cardinality of this set which has been joined (union).
Am I close at all to it's meaning? If so, could you then have a big intersect symbol to intersect the sets produced. There is also an example later with $\displaystyle b \in C$ under the big union symbol, is this just a condition for the union operation?
You realize that it is very hard to read the image.

The notation $\displaystyle |A\cup B\cup C|$ stands for the number of elements in at least one of $\displaystyle A,~B,\text{ or }C$.

It equal to $\displaystyle |A|+|B|+| C|-|A\cap B|-|A\cap C|-| B\cap C|+|A\cap B\cap C|$.

Now please tell us what you need explaining.

3. ## Re: Hey guys! What operation is this symbol?

Originally Posted by philleonard
As far as I can tell from the description it is the union of all the sets $\displaystyle$A_{x}$$where \displaystyle x is an element of \displaystyle X. Yes, \displaystyle \bigcup\{A_x:x\in X\} is the union of \displaystyle A_x for all \displaystyle x\in X. Originally Posted by philleonard could you then have a big intersect symbol to intersect the sets produced. Yes, \displaystyle \bigcup can be replaced by \displaystyle \bigcap to mean the intersection of all \displaystyle A_x. Originally Posted by philleonard There is also an example later with \displaystyle b \in C under the big union symbol, is this just a condition for the union operation? The big union symbol \displaystyle \bigcup is used in two ways. One can write \displaystyle \bigcup A if A is a family of sets: \displaystyle A=\{A_1,\dots,A_n\}. In this case, \displaystyle \bigcup A means \displaystyle A_1\cup\dots\cup A_n. Alternatively, by analogy with the summation symbol \displaystyle \sum, one can write \displaystyle \bigcup_{i\in I}A_i to mean the union of \displaystyle A_i for all \displaystyle i\in I. Thus, \displaystyle \bigcup\{A_x: x\in X\}=\bigcup_{x\in X}A_x. 4. ## Re: Hey guys! What operation is this symbol? Originally Posted by philleonard As far as I can tell from the description it is the union of all the sets \displaystyle A_{x}$$ where $\displaystyle x$ is an element of $\displaystyle X$. The lines being the cardinality of this set which has been joined (union).
That is correct. The |...| represent the magnitude of that set.

5. ## Re: Hey guys! What operation is this symbol?

Click on the image for a larger view please. Thanks for taking time to explain that though.
Edit: Sorry just seen all the new posts too, will read now. Thanks

6. ## Re: Hey guys! What operation is this symbol?

Thank you so much @emakarov Fantastic explanation!