this post was submitted on 14 Mar 2024
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Putting things in base 10 is also a definition. Digits aren't special.
Was going to say the same. Also π isn't infinite. Far from it. it's not even bigger than 4. It's representation in the decimal system is just so that it can't be written there with a finite number of decimal places. But you could just write "π". It's short, concise and exact.
And by that definition 0.1 is also infinite... My computer can't write that with a finite amount of digits in base 2, which it uses internally.
So... I'm crying salty tears, too.
[Edit: And we don't even need transcendental numbers or other number systems. A third also doesn't have a representation. So again following the logic... you can divide a cake into 5 pieces, but never into 3?!]
Not sure where you're going with the decimal thing. Pi had infinite digits in any integer base because it's irrational.
I thought that was the joke in the comic? That we can't know numbers exactly that have an infinite decimal expansion. That'd be true for some rational numbers like a third, if you change the basis of the numeral system it'd be different numbers. And irrational numbers too if you have a integer base. But I'd argue how we write down a number isn't what determines exactness or 'infinity' by the words of the comic.