# What does the expression x in RR mean ?

Mar 12, 2017

A real number is any rational or irrational number.

For example: $\pi , e , 2 , 4 , - 78 , \frac{1}{2} , \frac{23}{6}$ and so on

It means that $x$ is an element of the set of real numbers which we symbolize with $R$.

Mar 12, 2017

It usually means:

"$x$ is a member of the set of real numbers"

or more simply:

"$x$ is a real number"

#### Explanation:

• $\mathbb{R}$ usually denotes the set of Real numbers.

• $\in$ denotes membership.

So $x \in \mathbb{R}$, means that $x$ is a member of the set of Real numbers. In other words, $x$ is a Real number.

Related expressions are:

• $\forall x \in \mathbb{R} \text{ }$ meaning "for all $x$ in the set of real numbers". in other words: "for all real numbers $x$".

• $\exists x \in \mathbb{R} : \ldots \text{ }$ meaning "there exists a member $x$ in the set of real numbers such that ..." or "there exists a real number $x$ such that ...".

In some kinds of constructive mathematics, where speaking of "the set of Real numbers" is considered a little presumptuous, the expression "$x \in \mathbb{R}$" may be read as "$x$ is a real number" and $\forall x \in \mathbb{R}$ understood as "for any real number $x$", etc., avoiding the concept of a completed set of real numbers.