What does the notation C = C1 U C2 mean?

[tarmon.gaidon]

Hey Everyone,

This may be a silly question and I am able to interpret the intention of the notation but I am just curious exactly what it is.

I am attaching an image of the page out of my textbook and it is near the bottom. C = C1 U C2.

Sorry again if this is a silly question, I just wanted to make sure I understand this notation outside the context of this problem. I am sure I have seen it before but I am still not sure.

Thanks,
Rob

 

[Mark44]

Your attachment hasn't been approved yet.

Are you asking about C1 U C2? The U symbol is "union".

x is an element of A U B if x is an element of A or x is an element of B. The "or" really means "and/or" to include elements that might be in both sets.

For example, if A = {1, 2, 3, 5, 8} and B = {3, 6, 9, 12}, then A U B = {1, 2, 3, 5, 6, 8, 9, 12}.

Another set operation is "intersection" $\bigcap$. x is an element of A $\bigcap$ B if x is an element of A and x is an element of B. Using the same example, A $\bigcap$ B = {3}.

 

[HallsofIvy]

In this case $C_1$ is the straight line from (0, 2) to (3, 2) and $C_2$ is the straight line from (3,2) to (3,5). "$C= C_1\cup C_2$" is the two paths put together: to integrate along C, integrate along $C_1$ and $C_2$ and add the two integrals.