# Mystery of Infinity-2

We all know the famous identity:

$$0.9999\ldots{ }\ldots{ }\ldots = 1$$.

Here the numbers on the both sides are in base $$10$$.

One special thing here about $$9$$ is: in this case, $$9$$ just one less than the base $$10$$.

So, noticing this special property, one can make the conjecture that

The equality $$0.ccc\ldots{ }\ldots{ }\ldots = 1$$ is true in every base $$b \geq 2$$, where $$c$$ is the largest digit in base $$b$$, equivalently, $$c=b-1$$.

Is this conjecture TRUE?

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