Answer:
0.111111....... < 0.125
Step-by-step explanation:
Since, a number defined by,
A = {\(\frac{1}{n}\) : nā N} lies between 0 and 1,
That is,
\(\frac{1}{9}\) ā A,
\(\frac{1}{8}\) ā A,
Also, in the number line the numbers are arranged in increasing order from left to right,
āµ \(\frac{1}{8}\) is right to \(\frac{1}{9}\) in the number line,
\(\implies \frac{1}{9}<\frac{1}{8}\)
\(\implies 0.1111.... < 0.125\)
Note : We take \(\frac{1}{9}\) because a fraction having numerator 1 and denominator 'multiple of 3' is always non terminating.