I think I know the answer - countably many, and intuitively it does make sense i.e. it wouldn't make sense that a number has uncountably many decimal digits (is that even possible). However, I've been trying to prove it in set theory and couldn't do it so please help. Thank you!
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$\begingroup$ It only has 10, so countably many. Though I suspect my interpretation isn’t what you’re trying to ask. $\endgroup$– Mark SavingCommented Dec 23, 2022 at 7:06
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You can count the decimal digits of any real number. Notice that any real number can be written in the form $x = \sum_{k=-\infty}^{+\infty} a_k \cdot10^k$ with $a_k \in \{0,...,9\}$.
The set $(a_k)$ refering to the digits of $x$ is countable and therefore the decimal digits of $x$ are also countable.
