this post was submitted on 14 Mar 2024
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suck it, math nerds (mander.xyz)
submitted 7 months ago by [email protected] to c/[email protected]
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[–] [email protected] 69 points 7 months ago (1 children)

Not true. If you define the circumference in terms of pi, you can define the circumference exactly.

[–] gmtom 7 points 7 months ago (2 children)

"Find" not "define"

[–] [email protected] 45 points 7 months ago (2 children)

Putting things in base 10 is also a definition. Digits aren't special.

[–] [email protected] 27 points 7 months ago* (last edited 7 months ago) (2 children)

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?!]

[–] [email protected] 4 points 7 months ago (2 children)

Can pi be expressed with a finite amount of digits in another number system?

[–] Donjuanme 21 points 7 months ago (2 children)

How about a pi based system, then pi is 1.

[–] 33550336 1 points 7 months ago

Possible, but then the diameter would be an irrational number

[–] [email protected] 10 points 7 months ago (2 children)

I don't think there's any technical reason we can't count in base pi

[–] [email protected] 2 points 7 months ago

I'm pretty happy with being able to write integers in a finite number of digits. Wouldn't want to give that up.

[–] [email protected] -1 points 7 months ago (1 children)

Well we need an integer base number system....

[–] [email protected] 8 points 7 months ago (1 children)

"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)

[–] [email protected] 1 points 7 months ago (1 children)

But it makes life harder

[–] [email protected] 1 points 7 months ago (1 children)

Not if you're mainly interested in counting multiples of pi.

[–] [email protected] 1 points 7 months ago

nπ is much better

[–] [email protected] 0 points 7 months ago* (last edited 7 months ago) (1 children)

Not sure where you're going with the decimal thing. Pi had infinite digits in any integer base because it's irrational.

[–] [email protected] 1 points 7 months ago* (last edited 7 months ago)

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.

[–] [email protected] 17 points 7 months ago

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)