# Set notation (union and intersection)

1. Oct 21, 2009

### DPMachine

1. The problem statement, all variables and given/known data

Find simpler notation for the two sets:

$$A= \bigcup^{\infty}_{j=0}[j,j+1]$$

and

$$B= \bigcap_{j \in Z}(R minus\ (j,j+1))$$

2. Relevant equations

3. The attempt at a solution

Not really sure what it means by "simpler notation"...

Does $$A=R$$ since the union of [j,j+1] would eventually cover the whole interval?

And $$B=Z$$ because the intersection of R minus (j,j+1) would only leave the integers because it is an open interval.

Last edited: Oct 21, 2009
2. Oct 21, 2009

### Office_Shredder

Staff Emeritus
For A you have the right idea, but is it really every single real number? Consider what the smallest element in A is.

For B, it looks like each of the sets that you are taking the union of is

R-(j,j+1)

Shouldn't each of those sets be a subset of B then?

3. Oct 21, 2009

### DPMachine

Sorry, for B, it should be an intersection. I just fixed it.

For A, I think it should be R+ since it starts at [0,1]..

4. Oct 22, 2009

### lanedance

R+ sounds good, for B wirite it in terms of its complement and use the fact an intersection of complements is then complement of the union

5. Oct 22, 2009

### lanedance

re-read your first post - sounds about right for the 2nd one

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