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?!]
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.
That doesnt make a difference. You can find the exact circumference of a circle, you just cant express it in the decimal system as a number (thats why we have a symbol for it so you can still express the exact value)
Not true. If you define the circumference in terms of pi, you can define the circumference exactly.
“Find” not “define”
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?!]
Can pi be expressed with a finite amount of digits in another number system?
How about a pi based system, then pi is 1.
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You’re correct.
For reference: https://en.wikipedia.org/wiki/Non-integer_base_of_numeration
Possible, but then the diameter would be an irrational number
I don’t think there’s any technical reason we can’t count in base pi
I’m pretty happy with being able to write integers in a finite number of digits. Wouldn’t want to give that up.
Well we need an integer base number system…
“A base is usually a whole number bigger than 1, although non-integer bases are also mathematically possible.”
https://simple.m.wikipedia.org/wiki/Base_(mathematics)
But it makes life harder
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.
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That doesnt make a difference. You can find the exact circumference of a circle, you just cant express it in the decimal system as a number (thats why we have a symbol for it so you can still express the exact value)