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I think you will quickly find that there are only 10 distinct digits found within pi.

This is a very base-10 mindset.

In fact, if we use base-π representation then π=1 and memorisation is trivial. QED.

Oh no, then if n=∞, there are infinite digits in pi!

Is life itself really more than a series of rather futile endeavours? The point is that futility is, luckily, orthogonal to being enjoyable.

Infinite? Only if you include duplicates...

Or if you include order, which is what was meant (that's called literal irony)