# Weird function that changes digits

Calculus Level 5

Let $$g(x)$$ be a function over the real numbers defined as follows. Each nonzero digit in the decimal expansion of $$x$$ will get changed to the digit that is $$1$$ less, and each zero digit stays zero. For example, $$g(25.370142) = 14.260031$$ and $$g(\pi) = 2.0304815424...$$

What is the size of the set of real numbers at which $$g$$ is not continuous?

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