ONE

X had a Q&A session with Buddha.

X: What is 0.9\;?

Buddha: 0.9 is \frac{9}{10}\;.

X: What is 0.99\;?

Buddha: 0.99 is \frac{99}{100}\;.

X: What is 0.999\;?

Buddha: 0.999 is \frac{999}{1000}\;.

\ddots

X: What is 0.99999....\;?

Buddha: What are the dots ?

X: The dots are all 9‘s. It means \forall n \ge 1, the n^{th} digit after the decimal point is 9.

Buddha: 0.99999... is

\sum\limits_{i=1}^{\infty}\frac{9}{10^i}

X: What is \sum\limits_{i=1}^{\infty}\frac{9}{10^i}\;?

Buddha: It is

1

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