I’m using the Twelve Days of Christmas (and perhaps a few extra days besides) to do something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on different techniques that I’ll use to try to convince students that .

Part 1: Converting the decimal expansion to a fraction, with algebra.

Part 2: Rewriting both sides of the equation .

Part 3: Converting the decimal expansion to a fraction, using infinite series.

Part 4: A proof by contradiction: what number can possibly be between and ?

Part 5: Same as Part 4, except by direct reasoning.

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*Posted by John Quintanilla on December 22, 2014*

https://meangreenmath.com/2014/12/22/why-does-0-999-1-index/