Question

Express the following sets in the set-builder form.

$\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\mathrm{\dots }\}$

Answer 1

Definition : Set builder form : Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy.

Let $\mathrm{A}=\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\mathrm{\dots }\}$

Here the denominator is a set of natural numbers increasing linearly.

Thus set builder form is $\mathrm{A}=\left\{\mathrm{x}:\mathrm{x}=\frac{1}{\mathrm{n}},\mathrm{where}\mathrm{x}\in \mathrm{N}\right\}$

Hence, the set builder form of $\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\mathrm{\dots }\}$ is $\left\{x:x=\frac{1}{n},\mathrm{where}x\in N\right\}$.