Question

What does $\mathbb{R}$ equal in maths?

Answer 1

Hint: Intuitively, a real number $\mathbb{R}$ represents a point on the number line, or a (signed) distance left or right from the origin, or any quantity that has a finite or infinite decimal representation. Real numbers include integers, positive and negative fractions, and irrational numbers like $\sqrt 2 $ , $\pi $ and $e$ .

Complete step by step solution: 
In mathematics, $\mathbb{R}$ denotes real numbers. It consists of rational numbers $\mathbb{Q}$ i.e., natural numbers $\mathbb{N}$ , whole numbers $W$ , integers $\mathbb{Z}$ and irrational numbers $(\mathbb{R} - \mathbb{Q})$ .
Let $a$ and $b$ represent arbitrary real numbers. Then we can write,
The additive inverse or negative of $a$ is the number $ - a$ that satisfies $a + ( - a) = 0$.
The difference between $a$ and $b$ , denoted by $a - b$ , is the real number defined by $a - b = a + ( - b)$ , and is said to be obtained by subtracting $b$ from $a$ .
If $a \ne 0$ , the multiplicative inverse or reciprocal of $a$ is the number ${a^{ - 1}}$ that satisfies $a \cdot {a^{ - 1}} = 1$ .
If $b \ne 0$ , the quotient of $a$ and $b$ , denoted by $\dfrac{a}{b}$ , is the real number defined by $\dfrac{a}{b} = a{b^{ - 1}}$ , and is said to be obtained by dividing $a$ by $b$ .
A real number $a$ is said to be negative if $a < 0$ .
A real number $a$ is said to be non-negative if $a \geqslant 0$ .
A real number $a$ is said to be non-positive if $a \leqslant 0$.

Note: For any real number $a$ , the absolute value of $a$ , denoted by $\left| a \right|$ , is defined by
\[\left| a \right|=\left\{ \begin{align}
  & a,a\ge 0 \\
 & -a,a<0 \\
\end{align} \right.\]
If $S$ is a set of real numbers then, a real number $b$ is said to be a maximum of set $S$ or a largest element of $S$ if, $b$ is an element of $S$ and in addition $b \geqslant x$ whenever $x$ is any element of $S$ . The terms minimum and smallest element are obtained similarly.