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- How many zeros are there in the infinite decimal sequence of pi

Is there a way to prove if the 0s (or 1s 2s or 3s or ... or 9s) that are present in the infinite sequence of digits of pi in the decimal system are finite or infinite?

If they are infinite they are countable infinite or uncountable infinite?

My intuition tells me that they are countable infinite but cant find a way to prove it.

If they are infinite they are countable infinite or uncountable infinite?

My intuition tells me that they are countable infinite but cant find a way to prove it.