Element[ ] for real numbers

I was just wondering that one can easily check the presence of any number rational/irrational in $\mathbb R$ but I could not find if Mathematica supports any notation for open sets. The number of elements in $\mathbb R$ or open sets will be infinite and anyway $\mathbb R$ itself is infinite open set. So, I wanted to know

1. What is the algorithm that can be used to check for the presence of a number in $\mathbb R$ ?
2. How can one pick out one subset of $\mathbb R$ as some $(a,b)$ or $[a,b]$ and work with it ?

Any help is appreciated. Thanks.

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Look up Reals and Interval[]. –  Ｊ. Ｍ. May 16 at 13:14
rafiki -- it's not clear what question you are asking here -- if you can provide us with some code that you've tried or a more specific question, we might be able to help. –  bill s May 16 at 13:42
@J.M.: Thanks for hint JM. –  Blackbird May 16 at 18:23
@bills: I was wondering if mathematica supports analogy of open/closed sets so I was exploring. JM's hint helped me with relevant info. Thanks ! –  Blackbird May 16 at 18:24