it's a transcendental number. there is no "all" to the list of digits. i.e. there are an infinite number of digits.
taks
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It'd probably be more appropriate to refer to it as an irrational number. Transcendentals are a subset of irrational numbers, and a characteristic of an irrational number is that it cannot be expressed in rational form (no a/b). If it cannot be expressed in rational form, then it means there is an undefined, non-repeating amount of numbers to the right of the decimal.
It's just as impossible to count all the numbers of root(2) as it is Pi, but root(2) is not a transcendental.