Mathematica Mathematical notation

  • Thread starter Yegor
  • Start date
147
1
T is an index set. And for each [tex]t \in T[/tex] [tex] A_t [/tex] is a set
[tex]\bigcup_{t \in T} A_t = \{x : \exists t \in T with x \in A_t \}[/tex]
What means this [tex]\bigcup[/tex] symbol and entire expression?
And question on index set: is it used just for orderring any other set?
 

Galileo

Science Advisor
Homework Helper
1,989
6
It's the union. If A and B are sets, [itex]A\cup B[/itex] denotes the union of A and B. It's that set which contains all the elements of A and those of B. So
[tex]A \cup B = \{x|x\in A \vee x\in B\}[/tex]

To generalize this to a union of an arbitrary number of sets is easy. That's exactly what your expression is: the union of all [itex]A_t[/itex].
 
147
1
thank you very much, Galileo!
What about my guess about "index set"?
 

Galileo

Science Advisor
Homework Helper
1,989
6
I didn't understand what you meant exactly, but I think you have the right idea. The index set is just there to label the other sets. This way you can make T finite, countably infinite or uncountably infinite with the same notation. So the collection of sets A_t may be a finite, or infinite collection of any cardinality.
 
114
0
I just stumbled onto this post and it relates exactly to what I'm trying to figure out. This concept of an index set is very baffling to me. Can you give a little more detail on what exactly an index set is?
 

Related Threads for: Mathematical notation

Replies
8
Views
9K
  • Posted
Replies
7
Views
573
Replies
3
Views
2K
Replies
4
Views
3K
Replies
2
Views
15K
Replies
3
Views
1K
Replies
2
Views
44K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top