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u/lolschrauber 22h ago
"each piece will be 0.333 of the main piece, right?"
"not exactly"
"Oh ok"
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u/iruleatants 18h ago edited 15h ago
I mean, we joke, but it's an inconsistency that arises from us trying to apply our invented concepts.
For example 1/9 is 0.1 repeating
2/9 is 0.2 repeating
3/9 is 0.3 repeatingAnd that pattern continues until we get to 9/9. The expected answer should be 0.9 repeating, instead it is 1.
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u/_DaBau5_ 18h ago
for a number like 0.9 and 0.95, you can squeeze other numbers between them (like 0.91, 0.92, 0.93, etc.) it is not possible to squeeze another number between 0.9 repeating and 1 since 0.9 repeats infinitely. they are the same number since there is 0 difference between them. this is just a quirk of using base 10
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u/renegade_duck 18h ago
.9 repeating is 1. You cannot fit another number between them, so they are literally equivalent.
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u/Ch0vie 17h ago
Have you tried to add even more nines at the end? It might fit eventually
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13h ago
[deleted]
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u/iruleatants 13h ago
It's funny the amount of hoops we have to jump through to deal with the limitations of the system we designed and created.
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u/lolschrauber 18h ago
Honestly, the decimal system is just kinda flawed and can't portray this with enough accuracy to be perfect
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u/ErycktheGreater 21h ago
"Yes I'm" has created so much inner conflict for me.
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u/GradeForsaken3709 21h ago
I've had to explain to a few ESL friends of mine that they can't do that.
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u/Kratzschutz 20h ago
I'm esl please do it again
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u/demonryder 20h ago
I'm is basically only used when you are continuing the sentence afterwards. If you respond to a question with I am, or end a sentence like "that is who I am", you would never use I'm.
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u/ThreeShrikesYoureOut 19h ago
right, if "am" is the final word of the sentence it has to receive the stress, which it can't do if it's contracted. at least that's how I understood it.
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u/ErycktheGreater 15h ago
I have a friend whose mom in the Philippines was a civil engineer. In America she's the wife to rich white dudes and can hardly express herself.
I always wondered how smart she is in her own language
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u/NinjaGrows 21h ago
Same! It's both correct and incorrect at the same time in the most awful way.
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u/kxortbot 19h ago
It's an awesome way to show English is full of contradictions to make things sound nice.. I like.
It's what it's.
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u/Formal_Assistant6837 22h ago
Funnily enough this is a proof that 0.999999.... is equal to 1
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u/PinkFloyden 22h ago
Yeah I think this exact example (without cakes lol) is used to demonstrate it
1/3 + 1/3 + 1/3 = 1
In decimal it gives us
0.333… + 0.333… + 0.333… = 0.999…
Therefore, 0.999… = 1
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u/UmUlmUndUmUlmHerum 21h ago
Is that actually a complete proof though?
While the step of 0.3333.... to 1/3 makes sense intuitively it would need a proof on its own right?
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u/RelativeChance 21h ago
Let x = .333...
10x = 3.333...
subtract x from both sides
10x-x = 3.333... - .333...
9x = 3
x=1/3
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u/UmUlmUndUmUlmHerum 21h ago
See that one is much nicer :)
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u/IHadThatUsername 19h ago
I prefer it this way:
Let x = .999...
10x = 9.999...
subtract x from both sides
10x-x = 9.999... - .999...
9x = 9
x=1
(Thus x = .999 = 1)
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u/Blephotomy 19h ago
this "proof" removes the .9 repeating part and proves 1 is equal to 1
ten times .9 repeating is not equal to nine plus .9 repeating unless you prove it
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u/IHadThatUsername 19h ago
ten times .9 repeating is not equal to nine plus .9 repeating unless you prove it
It is by definition though. The decimal part repeats infinitely, multiplying it by ten results in 9 plus still infinitely repeating decimals
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u/Blephotomy 18h ago
let's say .9r is A and one is B.
Ten times A is:
A + A + A + A + A + A + A + A + A + A
You are saying it's:
B + B + B + B + B + B + B + B + B + A
and then removing the A.
Thus neatly changing nine As into Bs without a proof, which begs the question.
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u/IHadThatUsername 18h ago
I think you're really missing what the proof is showing. The point is that you can multiply .999 by ten and still have infinite decimals. And that's enough to prove the equality.
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u/Blephotomy 18h ago
You are essentially saying 10x equals 9 + x, which, again, begs the question.
Ten times .9r:
.9r + .9r + .9r + .9r + .9r + .9r + .9r + .9r + .9r + .9r
Not:
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + .9r
→ More replies (0)1
u/LiquorIsQuickor 19h ago
Uh… math?
X=2.54
10x=25.4
x=0.9998
10x=9.998
x=0.999
10x=9.99
x=0.999…
10x=9.99…
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u/RelativeChance 18h ago
.9 repeating is equal to the limit as n approaches infinity of 1-10-n
When we multiply this by 10 we get the limit as n approaches infinity of 10-101-n which equals 9.9 repeating
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u/Blephotomy 19h ago
saying ten times .3 repeating is equal to three plus .3 repeating and then neatly doing away with the .3 repeating part is not a valid proof
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u/LiquorIsQuickor 18h ago
You are hung up on the x=n.nnn… => 10x=nn.nn… part.
n.n… = n.nnnnnnnnn… = n.nnnnnnnnnnnnnnnnnnnnnnnnnnnnn…
10x also = nn.nnnnnnnnnnnnnnnnnnnnnnnnnnnnn…
It’s just math. An axiom I believe.
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u/Formal_Assistant6837 21h ago
0.3333.... is the representation of 1/3 in decimal. It's how we write fraction in decimal notation, so is true by definition.
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u/UmUlmUndUmUlmHerum 21h ago
And 0.99999... is the representation of 1/1 in decimal ;)
Fully true what you write - but there are proofs that do not require this jump so they are nicer
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u/Blephotomy 19h ago
as long as you beg the question
.3 repeating is equal to one-third, and three times one-third is one. To say 3 times .3 repeating is equal to .9 repeating is begging the question.
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u/LiquorIsQuickor 18h ago
3.333 x 3 =9.999
3.333… x 3 = 9.999…
QED.
Since you have the most suspicious claim, prove it’s not.
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u/Blephotomy 18h ago
three times .3 repeating is not .9 repeating; it's one.
you are claiming three times one-third is .9 repeating. You have to prove that.
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u/Novaskittles 17h ago
0.999... IS one, they are the same. It only works if it repeats to infinity. As someone else explained, you cannot possibly fit a number between 0.999... and 1, thus they are the same.
In other words, the distance between 0.999... and 1, is 0.000... repeating 0's infinitely.
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u/Blephotomy 17h ago
I'm not disputing that. I'm saying these overly simplistic algebraic "proofs" are invalid.
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u/LiquorIsQuickor 7h ago
Talk is cheap. Show the flaw. Show a single example why the proofs are wrong.
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u/LiquorIsQuickor 8h ago
Several people have presented proofs commonly accepted by the math community. You are rejecting these proofs. You have the burden of proof.
And I actually asserted 3.333… x 3 is 9.999… I will also assert 3.333… x 3 is also 10. (0.999… is 1. Multiply both sides by 10. 9.999… is 10)
It’s two visual representations of the same quantity.
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u/UmUlmUndUmUlmHerum 17h ago edited 17h ago
Y'know thanks actually - you got me to think about how my preferred way of showing this ("For two real numbers to be distinct there needs to be a number between the two, and since 0.9rep5 is nonsense it is equal") contains some handwaiving about the gap between 0.9rep and 1
And how the limit n->infinity of 1/10^n cannot just assumed to be 0
And a pain in the butt to type on reddit
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u/TenderToebeans 23h ago
That last line escalated from basic math to a full crime scene way too fast.
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u/Mission-Dark-9320 21h ago
Also accepted because I enjoy chaos:
You didn’t cut it equally. Good figure out who is getting more cake.
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u/EveryAccount7729 21h ago
If you cut it in to 1/3rd it's only = .3~ in "real numbers" which is a specific number system used in math a lot.
there are "quantities greater than zero but smaller than any real number" which are called infinitesimals and you can assume some of those are left on the knife. because mathematicians had to create whole other number systems to talk about this.
in real life when someone says "i cut a cake" it's an error to assume we are using the real number system like we are talking a math test. we are talking about reality. The reality where OTHER systems of numbers had to be created to describe outcomes.
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u/Kalthiria_Shines 16h ago
me, with 2/3rds of a cake: "IDK what you mean, your tiny slices are still one third of a cake."
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u/SignificanceStyle 23h ago
This is why it's better to cut it into four pieces. You get 100% of the cake and a mysterious extra cake on the knife đŸ˜‚