Weird function that changes digits

Calculus Level 4

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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