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All numbers, are fundamentally stand ins for the way they are calculated. "3" is a stand in for the calculation of adding 1 to 2, for example.
Maybe that sounds funny, but I think its essentially true.
So, numbers with infinite decimals are just numbers that represent a non-terminating calculation. It would go on forever, if you were to calculate it forever. But of course, you wont calculate it forever.
I think this basically resolves the confusion as to how any mathematical object can have infinite detail. It doesnt actually, but we can prove that the process by which the number is calculated would go on infinitely.
