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[-] porkins@sh.itjust.works 52 points 1 year ago

Because it’s not .333, it’s .333… or 1/3 and it’s not .999, it’s .999…, which is the same as 1 🫠. Primes and fractions are weird.

[-] areyouevenreal@lemm.ee 77 points 1 year ago* (last edited 1 year ago)

The fun thing is this is just a consequence of how we write numbers. If you used base 12 1/3 would be 0.4. Obviously 0.4 + 0.4 + 0.4 in base 12 is 1.0, so 3 x 0.4 = 1

What's even more fun is that things like 1/5 or 1/10 are recurring decimals in base 12.

[-] Mnemnosyne@sh.itjust.works 39 points 1 year ago

You know, this explanation makes it make sense to me a lot more than most of the others I've ever gotten.

[-] MxM111@kbin.social 18 points 1 year ago

I don’t get it. Are you saying the knife is clean?

[-] porkins@sh.itjust.works 12 points 1 year ago

Yes. The knife is clean if we are cutting exact thirds. As one other user mentioned, base-10 doesn’t allow prime fractions to be conveyed cleanly, so we use repeating decimals to imply that it is a fraction.

[-] ieightpi@lemmy.world 10 points 1 year ago

Either we live in a world where .333 is correct or we live in a world where knives come out clean when cutting a cake. We can't have both

[-] lud@lemm.ee 6 points 1 year ago

I will take the world with clean knives any day.

[-] RizzRustbolt@lemmy.world 4 points 1 year ago

So that's a no on the infinite cake universe?

Lame.

[-] Caitlynn@feddit.de 3 points 1 year ago

It's a flaw in how we decribe our numbers

[-] myslsl@lemmy.world 5 points 1 year ago

It's not even really a flaw. Just a property. In some sense we've lost the property of uniqueness of decimal representations of numbers that we had with other sets of numbers like integers. In another sense we gain alternate representations for our numbers that may be preferrable (for example 1=1.000... but also 1=0.999...).

[-] Karyoplasma@discuss.tchncs.de 3 points 1 year ago* (last edited 1 year ago)

Flaw is a bit harsh. Periodic, infinite decimals happen because the denominator is not a multiple of the prime factors of the base and thus will exist in any base.

[-] RizzRustbolt@lemmy.world 2 points 1 year ago
[-] Karyoplasma@discuss.tchncs.de 2 points 1 year ago* (last edited 1 year ago)

Infinity is not a number and even if you would use it as a base, you couldn't represent anything other than infinity in a meaningful way.

Infinity^0 is indeterminate and infinity^x with x>0 is exactly infinity.

this post was submitted on 04 Nov 2023
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Math Humor

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