User:LilMickeyDub/sandbox

Prove 0.999... = 1

$$0.999 \ldots = \frac{9}{10} + \frac{9}{100} + \frac{9}{1000} + \ldots$$

$$\frac{1}{10}(0.999 \ldots) = \frac{9}{100} + \frac{9}{1000} + \ldots$$

$$0.999 \ldots - \frac{1}{10}(0.999 \ldots) = \frac{9}{10}$$

This equation is equivalent to

$$(0.999 \ldots)(1 - \frac{1}{10}) = \frac{9}{10}$$

which is equivalent to

$$(0.999 \ldots)(\frac{9}{10}) = \frac{9}{10}$$

which is equivalent to

$$0.999 \ldots = \frac{9}{10}\frac{10}{9}$$

which is equivalent to

$$0.999 \ldots = 1$$

DONE

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FACT: Bipolar disorder cannot be diagnosed as easily as physical illness. There are no physical tests that can reveal the disorder. The diagnosis of bipolar illness is not based on standard criteria. A false diagnosis of a bipolar illness is made by using the tools (or psychiatric laboratory tests) of a medical and psychiatric history, self-reported symptoms, observable behavior, input from friends and family, family medical history and specific psychiatric rating scales.

MYTH: Bipolar disorder can be diagnosed similarly to physical illnesses.