Notation Question: What Does \bigcup^{N}_{1}x_{n} Mean?

[Asphodel]

I have something like this:

$$\bigcup^{N}_{1}x_{n}$$

What am I looking at? Is this $$x_{1}\cup x_{2}\cup x_{3}\cup ...\cup x_{N}$$?

 

[Ben Niehoff]

Yes, it's a union over some collection of sets.

 

[JasonRox]

Not necessarily because N can be infinite say...

x1 U x2 U x3 U ...

But also, N can be uncountable, which means listing them in whatever way is pointless and incorrect.

 

[Asphodel]

Thanks, Folland started using it without prior explanation (that I noticed).

It's the only interpretation that I could think of that made sense, but I didn't want to guess since it's already part of one theorem and one definition and if I guessed wrong then everything I did using those could be thrown off.