# Thread: What set is the set I?

1. ## What set is the set I?

I'm reading a book at the moment and it mentions a set $\displaystyle I$ but doesn't define what this set is. Is there a general meaning for this set $\displaystyle I$?

I'll post the context as it may be helpful

Let $\displaystyle X$ to be generated from $\displaystyle f(x)$ where $\displaystyle x \in I$

Any help would be appreciated.

2. Originally Posted by alan4cult
I'm reading a book at the moment and it mentions a set $\displaystyle I$ but doesn't define what this set is. Is there a general meaning for this set $\displaystyle I$? I'll post the context as it may be helpful
Let $\displaystyle X$ to be generated from $\displaystyle f(x)$ where $\displaystyle x \in I$
There is absolutely to give a firm answer to your question.
If I were to guess, I would say that $\displaystyle \mathscr{I}$ stands for the irrational numbers.

3. There is absolutely to give a firm answer to your question.
I think you accidentally the whole sentence.

I think that I is some arbitrary index set, as in: Consider a family of subsets of natural numbers $\displaystyle \{A_i\}_{i\in I}$. That's why the author must have forgotten to describe it.

4. The (closed) unit interval is often denoted by $\displaystyle I$, and from your context I feel this is most likely. That is, the set of real numbers between 0 and 1 inclusive, $\displaystyle [0, 1]$.

If not, my second guess would be an index set; I've never seen the complex numbers denoted by $\displaystyle I$ (although that doesn't rule it out).

Also, have you tried looking for a `notation' section in your book? They're often at the back with the index and references, or immediately after the contents.

5. I've checked the book and it doesn't define $\displaystyle I$ anywhere. An interval would make sense if we wanted to sample only x's that fall with in the interval $\displaystyle I$, however I think it maybe an arbitrary interval rather than [0,1]

6. If you post more about the context, maybe we can recognize its use.

7. The context is the Acceptance-Rejection Method in Random Variable Generation. $\displaystyle X$ is the variable I wish to sample and it has probability distribution $\displaystyle f(x)$, $\displaystyle x \in I$