What is an Index Set and How is it Defined?

[Buri]

Can someone give me a precise definition of what an index set is? I have never seen it defined.

Thanks!

 

[micromass]

An index set is just a set which only use is to index something.
For example, in $$\bigcup_{i\in \{1,2\}}{A_i}$$, the set $$\{1,2\}$$ is an index set.

Sometimes you'll see "Take an index set I and consider the union $$\bigcup_{i\in I}{A_i}$$..." This just means that you can take any set and consider the union. There is nothing special about I, it can be about anything.

An index set is like an integration variable, it's only use is to make your notation work. For the rest, it isn't used.

 

[HallsofIvy]

Before defining "index set" you will have to define "index"!

 

[Buri]

Before defining "index set" you will have to define "index"!

Could you define both then? lol