Question

Write the set $A=\{\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6},\frac{6}{7},\frac{7}{8},\frac{8}{9}\}$ in the set-builder form.

Answer 1

The set $\{\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6},\frac{6}{7},\frac{7}{8},\frac{8}{9}\}$

Each number in the given set has the numerator one less than the denominator.

Also, the numerator begin from 1 & don't excel 6

Hence, in the set - builder from the given set is

$x:x=\frac{n}{n+1},$ where n is rational number & $1\le n\le 6$