February 9, 2011

1.0 = 0.999...


Perhaps the most widely-held misconception in mathematics is that every number has a unique decimal representation.

In fact, every rational number with a terminating decimal representation has also a non-terminating decimal representation.

For example: 1.0 = 0.999....

Don't believe it? Here is a simple proof:
1/3 = 0.333...

3*(1/3) = 3* (0.333...)

1 = 0.999...
Indeed.


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