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I think your definition of "know" is unreasonably strict. Especially because we can write out pieces of algebra that are exactly pi.

I think it's reasonable to say we can't truly measure pi, though.

And you can neither know nor measure a random real.

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Hmm, I should say "the numerical value of pi in base 10" (or really any rational base), even if we were to weaken that with the qualifier "a to arbitrary degree of precision". We know pi in the sense of "a unique real number satisfying many useful properties".

Isn't "3.14" pi to an arbitrary degree of precision? Or am I misreading that.

> We know pi in the sense of "a unique real number satisfying many useful properties".

We know it a lot better than that. We have efficient programs that output the numerical value of pi for as many digits as you want.

There's a bunch of real numbers we can identify that are far harder to make use of or approximate, and don't have easy exact description of their value.

> we can write out pieces of algebra that are exactly pi

Sure, but how would you compare those against a measurement?

That depends on how you're measuring. But the second paragraph of that post already says you can't truly measure pi.

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