Union and Intersection of sets

In summary, the conversation discusses finding the union and intersection of sets A_i with elements (0,i), representing the real numbers x with 0 < x < i. The individual was initially confused by the notation, but was instructed to draw a picture and make a conjecture about the answer, with the help of others.
  • #1
Goldenwind
146
0

Homework Statement


a) Find: [tex]\bigcup_{i=1}^{\infty}} A_i[/tex]b) Find: [tex]\bigcap_{i=1}^{\infty}} A_i[/tex]

Where [itex]A_i[/itex] = (0,i), that is, the set of real numbers x with 0 < x < i

I was doing okay when they gave me [itex]A_i[/itex] = {i, i+1, i+2, ...}, but now that they're giving me (0,i), and introducing x, I'm getting confused.
 
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  • #2
Just noticed that I placed this in the wrong forum. I usually come to the Physics forum, however this time I meant for Calculus.
Tried to find a way to delete or move it, but not finding a way.

If an admin finds this, just delete it. I'll post it in the proper forum.

Apologies.
 
  • #3
Try making a picture. Draw a long line, this is the set of all real numbers. We indicate an open interval (a, b) by putting a bracket ( at the point a, and a bracket ) at the point b. Also see this webpage.
Now draw some intervals (0, 1), (0, 2), (0, 4) and look at their intersection and their union. Post a conjecture about the answer, we'll help you prove it.
 

What is the definition of union of sets?

The union of two sets A and B is the set of all elements that are present in either A or B, or both.

What is the definition of intersection of sets?

The intersection of two sets A and B is the set of all elements that are present in both A and B.

How is the union of sets represented?

The union of sets can be represented using the ∪ symbol, where A ∪ B represents the union of sets A and B.

What is the difference between union and intersection of sets?

The main difference between union and intersection of sets is that union combines the elements from both sets, while intersection only includes elements that are common to both sets.

Can the union and intersection of sets have the same result?

Yes, if the two sets are identical, their union and intersection will have the same result, which is the set itself.

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