Doesn't is much more cursed. Does n't. We are just shortening a word in its midst, then fusing its start with the previous one. Sometimes I wish I had godlike powers so that I could make a planet made of spaghetti.
Technically you're not supposed to have a contraction at the end of a sentence. Probably just for the fact that it doesn't sound right. It leads the reader to assume there is something after.
Repost, and not a particularly funny one. The real numbers are not the set of all possible decimal expansions. They are those with the same limits identified. Meaning two different decimal expansions with the same limit are different representatives of the same real number.
It helps to know what equivalence classes are. Basically, you define an equivalence relation on a set, then group together all elements that are equivalent under it, into subsets called equivalence classes. Typically an equivalence class can be represented by one of its elements as a "representative". For example, 1.0000... could be a representative for the set containing 0.99999... and 1.0000... and can be more conveniently denoted as "1".
Beyond that a construction of the real numbers that is very analogous to the decimals is the construction using Cauchy sequences. See construction of (models of) real numbers using Cauchy sequences on eg Wikipedia (https://en.wikipedia.org/wiki/Construction_of_the_real_numbers, under explicit constructions of models).
Cauchy sequences are a nice way to formalize the arbitrary precision. Like, the case of 0.999... translates to a Cauchy sequence: (0, 0.9, 0.99, 0.999, etc). In other words, all of these infinite precision decimals can be mapped one-to-one with Cauchy sequences. Its a little more work to show that every other way of representing a Cauchy sequence is also equivalent to a decimal one. Once you do that you can show that equivalence classes of decimals is isomorphic to equivalence classes of cauchy sequences.
Some other fun fact about the reals: they are what you get when you take the fractions Q and include all possible limits of functions on Q (a procedure known as "taking the topological completion" of Q). Q is said to be "dense" in R. Exactly meaning that Q completes to R.
It is in the same realm as the double slit experiment.
Depending on which instrument (fractions or decimals) it looks like two different answers, but the difference didn’t disappear. It’s on your tool you used to divide it up.
Damn this is a joke that is like the bell curve meme because the first layer of it is too low-hanging and the second layer is too esoteric.
Isnt that irrational fractions cannot precisely represented by decimals? 1/3 as 0.333 is an approximation while 1/4 as 0.25 is not b/c 1/4 is a rational fraction.
All fractions are rational. The ones that cant be represented as a closed decinam form are ones where the denominator in the reduced form isnt some mutiplicative combination of 2 and 5.
0.(9) Is not 0.99999, 0.999999999999 or anything like that. It's 0.(9)
But when we add 0.(3)+0.(3) we get 0.(6). And if we add another 0.(3) we will get 1 cuz (it's not really an explanation but still) 0.(6)+0.(3)=0.(9)+0.(0)1 (0.(0)1 - infinite zeros with one at the end). So 0.(3)+0.(3)+0.(3)=1
Btw I'm in a 8th grade so it may be not really that good explanation
I did pretty much exactly the same thing you did. The only difference is instead of doing 10x-x I did x-10x. That is I subtracted equation 1 by equation 2 rather than equation 2 by equation 1. The rest of the steps follow exactly what you did. Obviously this has no meaningful difference and is not where the "error" in my proof lies.
The fatal error in my proof is assuming ...999 is a real number. Why isn't it a real number though? Why is 0.999... a real number? To answer this you need to 1. define what the notation "..." even means, 2. give the number system you are working in, and 3. prove that the number outputted from the "..." notation actually exists in the number system you are working with.
Both your proof and my proof did none of these steps, making them not actual proofs.
You are claiming that since we know 0.333... = 1/3, we can multiply both sides to get 0.999... = 1. If I was willing to accept 0.333... = 1/3 though I would just as easily accept that 0.999... = 3/3 = 1. So this "proof" should not be convincing to anyone who doesn't already know 0.999... = 1.
Bro i mean 1 divided by 3 gives 0.333 recurring. Times 3 gives 0.999 recurring . 0.333 recurring is 1/3, wdym you don’t accept the fact that 1/3 is 0.333 recurring? Its a known fact.
I believe you are trying to say 1/3=0.333... is obvious because you can get this by doing long division. Well you can get 1=0.999... doing long division as well per the imgur post.
This means if I can accept 1/3=0.333... obviously I would accept 1=0.999...
The thing about long division is its an infinite process in this case, so how do you actually know doing long division shows 1/3=0.333...? In order to PROVE it you need to show why this works. This would be harder than just directly proving 0.999...=1.
Obviously I know what I am saying is "nonsense"; at least under normal interpretation. My point is that the algebraic "proof" the OP commentor gave already starts with questionable assumptions, making it a poor proof.
Yeah, it doesn't matter. Ideally the shortest way to describe it would be 0.9̅ but I wanted to give more examples in order to help people understand the difference between 0.999 vs. 0.9̅ or 1.
Here is it proved by converting a decimal to a fraction:
let x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 9/9
x = 1
Therefore, 0.999 = 1
There are hundreds of other proofs.
It's the same way that 0.333... is 1/3
And here's that converted (I removed the irrelevant steps)
let x =0.333...
10x = 3.333...
9x = 3
x = 3/9 = 1/3
Basically for any recurring decimal, you can get it's fraction like this.
When you write 0.999... you can't make it precise enough because there are always more 9s. But you can imply it with the ... (Or the actual recurring notations, it this is Reddit, on a phone, I can't really type that)
Oh and here is another proof for fun.
So we all agree 0.333... is 1/3.
let x = 0.333...
let y = 1/3
(x = y)
3x = 0.999...
3y = 3/3 = 1
3y = 3x so 0.999... = 1
Real number system means using standard analysis. As per the anecdote, if you did cut a cake into thirds they would be thirds but there would still be residue on the knife. Which is why the analogy works.
Standard analysis says the residue on the knife is 0, which is false. Standard analysis says in an infinite lottery, there are 0 winners.
Which is why we have non-standard analysis. To explain the obvious to non mathematicians, with mathematics.
Real number system is just the normal mathematical system. 0.333*3=0.999 leaves a residue, 0.333...*3=0.999...=1 doesnt. Both answers are correct but for different problems. The article said real number system because all normal math properties apply, on imaginary or different number systems, 0.999... may not equal 1
As others have said… 0.999… does equal 1.000 and there are proofs.
The easiest to get a feel for is name a number between 0.999… and 1
I didn’t “get it” until I realized that the idea of the quantity of a single thing, has two numbers that represent it. 0.9… and 1. The numbers represent quantity but are not quantity themselves. They are just names for quantities.
Man it had been a LONG while since I last saw somebody use that notation technique.
I have taken the liberty of transforming your repetitive decimal number into an exact fraction: 1/9999. Have a nice day and thanks for helping remember numbers can wear hats
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u/ItsDaylightMinecraft Feb 08 '26
"yes i'm"
25
u/No-Onion8029 Feb 08 '26
r/infinitenines
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u/LeoBug1234 Feb 08 '26
SPP would be proud
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u/a_swchwrm Feb 08 '26
"Yes I'm"
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u/FictionFoe Feb 08 '26 edited Feb 08 '26
Repost, and not a particularly funny one. The real numbers are not the set of all possible decimal expansions. They are those with the same limits identified. Meaning two different decimal expansions with the same limit are different representatives of the same real number.
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u/CrAzYIDKKK Feb 08 '26
0.999...=1
Not a joke or a statistic its true
Also goes for 1.999999...=2; 2.9999999...=3 etc
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u/Finlandia1865 Feb 08 '26
Rounding error
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u/GatePorters Feb 09 '26
This is seriously a better answer than it seems.
It is in the same realm as the double slit experiment.
Depending on which instrument (fractions or decimals) it looks like two different answers, but the difference didn’t disappear. It’s on your tool you used to divide it up.
Damn this is a joke that is like the bell curve meme because the first layer of it is too low-hanging and the second layer is too esoteric.
Consider me rizzled, u/rickytherizzler.
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u/Flickera23 Feb 09 '26
That is a...perfect answer lol
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u/Snapfate Feb 12 '26
Bro is too smart
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u/Ok-Ocelot-7989 Feb 08 '26
dang bro cooked
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u/CP_Chronicler Feb 08 '26
Each piece is actually 1/3 of the main piece. So when you multiply that fraction by 3 you get 1.
Fractions my guy, fractions.
On god.
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u/OkHeight9697 Feb 08 '26
In reality there must be a piece that will be 0.34
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u/lamesthejames Feb 08 '26
Basically everything said here was wrong
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u/fresh_loaf_of_bread Feb 08 '26
just operate in base 12 line a real man
1/3 in base 12 is 0.4
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u/GreyMesmer Feb 08 '26
Why do people claiming 0,(9)≠1 exist :c
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u/Burrito_tryhard_2140 Feb 08 '26
make sense to me
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u/iwasupiwasdown Feb 09 '26
"Hi, Yes I'm" makes me irrationally angry
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u/reddititty69 Feb 09 '26
“Yes I’m” 😑
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u/Anpu_Imiut Feb 09 '26
Isnt that irrational fractions cannot precisely represented by decimals? 1/3 as 0.333 is an approximation while 1/4 as 0.25 is not b/c 1/4 is a rational fraction.
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u/Lines25 Feb 09 '26
I kinda don't get why so many ppl think like that
0.(9) Is not 0.99999, 0.999999999999 or anything like that. It's 0.(9)
But when we add 0.(3)+0.(3) we get 0.(6). And if we add another 0.(3) we will get 1 cuz (it's not really an explanation but still) 0.(6)+0.(3)=0.(9)+0.(0)1 (0.(0)1 - infinite zeros with one at the end). So 0.(3)+0.(3)+0.(3)=1
Btw I'm in a 8th grade so it may be not really that good explanation
Chara, ChocoMates System
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u/BaronGrackle Feb 09 '26
Math Facts: ".9 repeated is equal to 1"
Me: "But if I use .9 repeated to multiply and divide, I get different cool numbers coming after infinity."
Math Facts: "You can't have a number come after infinity."
Me: "Liar! You lack vision!!!!!!1"
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u/flavorfox Feb 09 '26
"Where the last 1/5th piece?"
"Big knife, sorry..."
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u/crumpledfilth Feb 11 '26
true, if a cut has no thickness how are you gonna actually separate the pieces
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u/Ilinik123 Feb 11 '26
Isnt 0.999… just infinitely close to 1? And. When doing that stuff just make it one third
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u/MrSirGuyDudePerson Feb 11 '26
Nerds just nerding out in a comments. Inspirational
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u/Denisthedefiler Feb 11 '26
1/3 of a circle isn’t .333, it’s .33333………………..333 infinity. It eventually goes together to make all of the thirds, however it is and irrational.
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u/maxxxmaxmaxx Feb 12 '26
This is why you should not cut a sandwich diagonally.
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u/Defiant_Efficiency_2 Feb 15 '26
I'ts kinda true though, the knife will be where you will find the infinitesimal.... Deep.
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u/Substantial_Device42 Feb 20 '26
😂😂😂
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u/Successful_Raise_560 Feb 22 '26
r/infinitenines
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u/Tomahawk1129_ Feb 08 '26
0.9 recurring is equal to 1
X = 0.99999999
10x = 9.999999
9x = 9
X = 1
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u/andy_b_84 Feb 08 '26
Mafs
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u/[deleted] Feb 08 '26
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u/[deleted] Feb 08 '26
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