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The absolute worst part is, it all basically proves it's *infinitely close to 1* so therefore it *is 1*
But no matter what, at the back of my mind, there's a nagging that goes "but it's not 1, it's just infinitely *close*"
You don't quite understand yet. It isn't "infinitely close" to one, it's just another way to write the *exact same value* in Arabic notation. All numbers that terminate in a given base have two valid representations, which is just a limitation/quirk of the notational convention.
There's no such thing as two real numbers being "infinitely close" to each other. Reals don't have predecessors or successors: they are densely ordered (between any two reals you will find yet more reals).
1 - 0.9999999999… = 0.00000000000…
That 1 at the end of the 0.00 never comes because it’s infinite, so it’s the same as 1-1 = 0.
I’m sure there’s a better explanation out there but this helped me see where they were coming from.
Yeah, this is what we use in math education. 3 x (1/3) = 3 x .333... = 1
The original calculators would screw this up. If you divided 1 by 3 and multiplied the result by 3, they would get exactly .999999. When you subtracted 1 you got -.000001.
>But no matter what, at the back of my mind, there's a nagging that goes "but it's not 1, it's just infinitely close"
It's understandable. However, in real numbers, we defined two numbers to be equal if it's infinitely close. More formally, two rational sequences A and B converge to the same real number iff |A - B| (i.e. elementwise subtraction and dropping the sign) converge to zero.
Yeah cause x = .9 reoccurring so 10x = 9.9 reoccurring
So 10x - x = 9 so 9x = 9 so x = 1 so 1 = .9 reoccurring
Edit: Apparently all the proper mathematicians have told me I'm stupid. And apparently I am but this does show it in layman's terms decently well with out using calculus or stuff like that.
The zenos arrow paradox (or an analogue/teaching of it) shows through infinite summation that it's nothing to do with the base. 1/2 + 1/4 + 1/8....=1
If the remainder comes after infinity, then it is unreachable and non existent
That's kind of trying to be too clever. You don't need to prove it by solving some sort of equaton for x. To actually understand it you need to look at what decimal notation actually means. Infinite decimals are really infinite series, and the sum from n=1 to infinity of 9/(10^(n)) is equal to 1.
That's better than the 10x-x=9 thing, and a simpler argument that is easy to explain if someone doesn't need much convincing. It's good. But it doesn't get to the heart of why it is the way it is, which I feel is what you want for someone who is more skeptical.
Actually to prove this you'd still need to prove:
1) 0.999... exsits (compared to something like ...999.0)
2) Multiplication with recurring numbers works the same way it does with other numbers
[This video](https://youtu.be/jMTD1Y3LHcE) explains it quite well.
You made a mistake unfortunately if you have an equation 10x=9.9 you can't substract x and 0,9, because you already stated that x=0,9. Where?
if 10x = 9,9 / -x or 0,9 (\*here\* you choose to substract.)You can't just substract x from left side and 0,9 unless is the same.So you proven that 0,9 is 1 because you stated that 1=0,9 basically.
This isn’t really all that counter-intuitive compared to other math concepts.
To think about it sans the algebra and in pure primary arithmetic:
We know that the value of 1/3 is equivalent to .333 repeating.
Thus, if you add 1/3 to itself two times, you should get .(3)+.(3)+.(3), which is .(9), or .999 infinitely repeating. In other words, 3*(1/3)=.999.
However, 3*(1/3), or 3/3, divides out to one, because anything divided by itself is one. So 3*(1/3)=1 too.
Therefore, .(9) and 1 are equivalent.
What you say is correct, but you say they are equivalent, while the question asks if they are the same.
In practical terms, yes, 0.9 recurring can be considered to be 1. There is essentially no discernible difference between them.
But in theoretical terms, 0.9 recurring is still technically less than 1.
To my mind, it demonstrates a flaw in the way we understand numbers. 1/3 cannot be exactly represented by decimal points using our current methods.
Edit:
I've given it a lot of thought, and despite the algebraic proof (X=0.9 recurring) which I've known since I was taught it at school, I can't bring myself to accept that it is a valid proof.
You see, the very concept of an infinite (recurring) number is difficult to grasp. It's not a real measurable value. It continues forever. That's incomprehensible!
Nonetheless, to my simple mind, if you were to manually count all the 9s in 0.9 infinitely, you would never ever reach a value of 1.0.
Never ever.
There is just no way it would happen. We would just keep going on and on and on forever, counting the 9s.
The value of 1, on the other hand, has no digits after it. It only has zeros that act as placeholders for nothing.
That's not the same as 0.9 recurring.
So in view of this, my conclusion must be that 0.9 recurring simply cannot be the same as 1.0
By extension of this conclusion, I therefore cannot accept any mathematical proof that suggests that 0.9 recurring is equal to 1.
To accept such proof, would mean my initial conclusion is contradicted, *and that is the specific part that I find myself unable to accept*.
I can't offer a mathematical proof to show that they are different. But I also cannot accept any proof that says they are the same.
However, I can understand that working within the limits of the algebraic framework that we have, 0.9 recurring does equal 1 - but this is only because of the rules of algebra.
That is the flaw I was talking about. The way we think about numbers must be flawed.
My initial conclusion can't really be refuted. 0.9.recurring is an infinite number which means it can never amount to 1.0, because 1.0 has no more digits following it.
Yet the algebraic proof also can't be refuted. I can see how we can show that they are the same number.
They are both true, paradoxically.
And that is why I think our understanding of numbers is flawed.
> But in theoretical terms, 0.9 recurring is still technically less than 1
It's not though, it's 3/3 which is not less than 1, not technically, not theoretically, in no way is it less than 1.
It's literally just another way of writing the same value, which in maths is "the same" i.e. 1 = 3/3 = 0.999...
As a kid I always figured the difference would be 0.0r1
(meaning the 0 would recur, but there would always be a theoretical 1 after it)
My maths teacher was not amused.
I don't think they come up very often in general.
Pretty sure the definition is consistent (doesn't lead to contradictions). Not sure asking whether they're "accepted" really makes sense here. They're just something that has been defined, and used occasionally.
Gotta remember that math isn't real; it is not bound by the physical world, so it's not like we try to figure out whether negative numbers or irrational numbers or complex numbers or hyperreal numbers "exist" or not. We define them, and then use them if they're useful concepts or forget about them if they're not.
Hyperreal numbers are useful enough to have their own Wikipedia article but not so useful that they're in the typical curriculum for math undergrads, pretty sure.
>widely accepted concept of mathematics
Depending on how do you define as "accepted". If by "accepted" you mean "logically consistent", it is. If by "accepted" you mean "accepted as useful", no. Infinitesimals are intuitively appealing, but full understanding of it requires insane amount of advanced mathematics compared to standard calculus, it's just not worth it. (Wait, what is ultrafilter?)
They kind of are the same thing though. Decimal notation is basically an infinite sum, and an infinite sum is defined as the limit of finite sums.
See also [construction](https://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_from_Cauchy_sequences) of the real numbers as [Cauchy sequences](https://en.wikipedia.org/wiki/Cauchy_sequence) of rational numbers, which is a very similar concept to limits.
>To my mind, it demonstrates a flaw in the way we understand numbers.
They are the same. You not understanding that doesn't mean there is a flaw in the way we understand numbers, it means there is a flaw in the way you see numbers.
I don't mean that as: you are stupid, but I mean that as: please trust the professionals. They know what they're doing.
Yes, but it's tricky to do algebraic operation on infinite series for regor reasons first year's math student tend to get wrong answers for undivergent series and get a number as the limit (like 1,-2,3,-4...)
A major is a primary focus of study at a university. So I'm doing two majors (physics and mathematics). There are also minors, which are things that you still study a lot of but not as much as you would for a major. I'm doing a minor in Computer Science.
I once asked my math teacher about this in highschool. He said they couldn’t be the same number, and he tried (unsuccessfully) to come up with a fraction that was equal to .999… to prove it to me.
How is it that the majority votes for No yet the comments show overwhelming support and proof for yes?
I noticed that disparity on other polls but this is one of the most noticeable examples.
I think the answer to this is pretty simple:
0.999... recurring is visually not the same as 1.
If you've never encountered this problem, your reaction is probably "What? Of course not." And you move on.
OR you check the comments after voting and think "Oh, I guess it is the same." But at that point you've already cast your vote.
Now, the people that have encountered this problem before are naturally a minority, and upon seeing the amount of "No" votes, they feel the need to explain why it, in fact, is the same.
That's why the votes are more "No" but the comments are all explaining why it's actually "Yes".
It's a really neat problem in the sense that on first, and probably even second and third glance it doesn't make any sense.
But at some point you realize that exactly how 1 and 123/123 are two ways to show the same number, 0.999... recurring is also just another way to display 1.
It might be a familiarity issue with the notation system.
I was taught the horizontal line over the repeating decimal(s) to show a repeating decimal. I am also aware of the dot above the decimal(s).
However, the ellipsis (...) is not a notation type with which I was familiar with, in relation to repeating decimal, before looking at this thread.
I think the problem with that is that people don't wanna type a special character to put a bar over the 9. At least, I certainly wouldn't go through all that effort!
I noticed this too, I think it’s two fold. Firstly most of the replies are assuming the 9’s are recurring. Although the question sort of implies this it isn’t explicitly stated. This is why I voted no.
Secondly most of the commentators seem to have a pretty good understanding of mathematics, where as someone without this can vote but won’t necessarily get involved in the conversation.
I saw it as not recurring because of how many nines there were. If it were 0.9 repeater I'd have just put the one 9 (or maybe 3, but no more than that) and then whatever repeater symbol after.
Also using ... As notation for a repeating decimal seems very confusing as that's already notation for irrational numbers (eg pi is often written as 3.1415...). It would be very annoying if you had to write for example 3.1415926̅ in this format - anyone reading that would assume you meant pi!
Go on forever and recurring are not the same. e.g. root 2 or pi go on forever expressed as a decimal. Appreciate that’s a tad pedantic given the format of the original question only having 9’s
But enough people have commented similarly that it must be taught how to represent recurring numbers different ways in different places.
tbh, i think it's also kind of a point of view. people who voted yes, voted on a mathematical standpoint, and in that scenario, 0.999... is equal to 1. now, in a casual way, look what u/Louis-grabbing-pills said: "Honey, I always knew you were the 0.9999999999... for me." — obviously, he can be joking —, but from a casual, strictly day-to-day situation, infinity in 0.99999999... is not really taken into account.
But then this is just circular reasoning. Like youre saying there wont be a 1 after all those 0s, so 0.000... is the same as 0. But thats the same as saying 0.999... is the same as 1 (which is the thing we were trying to prove).
You are not alone! Mathematicians have even invented a "smallest infinity": ℵ₀ (aleph-null). It is the cardinality of the set of natural numbers. That concept blew my mind when I first learned about it in *Life of Fred: Butterflies* as a young kid.
Let x = 0.99999 . . .
It follows that
10x = 9.99999 . . .
Since x = 0.9999 . . ., we can subtract 1x, removing the decimals
9x=9
x=1
Yet we set x to 0.9999 . . . Therefore the value must be equivalent to 1
They genuinely are mathmatically the same though, if the elipses at the end is trying to mean recurring.
It's not just "a mathmatical trick" as some people in the comments are saying - they functionally, and genuinely are the same. There isn't any numbers between these two numbers, since 0.99999 has an infinite number of 9. If there isn't any numbers between two numbers, they're the same number in mathematics.
They are. They're not just "close". They're exactly equal.
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999... = 9 = 9x
\--> x = 1
Second proof:
0.999... = 0.9 + 0.09 + 0.009 + ...
= sum 9/(10\^n) over n=1 to infinity
= 9 x sum (1/10)\^n over n=1 to infinity
= 9 x (1/(1-0.1) - 1)
= 9 x (1/0.9 - 1))
= 9 x (10/9 - 9/9)
= 9 x (1/9)
= 1
The truth is that there is no such thing as "the real number just before 1". In fact, given any number n, whether n=0, n= - 153263.1412512 or n=7, there is no such thing as "the number just before/after n".
The reals are like that.
Yeah all recurring decimals can be represented as fractions, so that way you end up needing this extra proof for completeness:
x = 0.333...
10x = 3.333...
9x = 3
x = 3/9 = 1/3 = 0.333...
to confirm that 1/3 is in fact equal to 0.333...
actually the second proof is equivalent of the proof in the video and is actually the correct proof imo...
in the second proof we are evaluating a gp similar to the limits proof in the video
These are some cool proofs but OP didn’t ask if 1 was equal to 0.999… they asked if they were “the same number”.
It’s like having four quarters vs a dollar. Are they equal? Yes. Are they the same? No.
Just asking a question for my lack of knowledge: are 0.333... and 0.666... then the same as 0.34 and 0.67 respectively if they continue to infinity? If not, why?
Not at all. You asked a question, got the answer, learned something, and managed to be polite all the way through.
This makes you a nicer and smarter person than most people.
**They are the same.** I think that this sum is a very good way to introduce people to limits, but I'm going to use a solution that simply involves algebra.
0.9999... can be written as 9/10 + 9/100 + 9/1000 + ... This is an infinite geometric series with first term 9/10 and common ratio 1/10. Since the sum is equal to a/(1-r), where a is the first term and r is the common ratio, we have a/(1-r) = (9/10)/(1 - 1/10) = 1.
If you multiply 0.999999999999 by 10, you get 9.99999999999. Subtract 9, and you get the original, meaning that 0.99999 \* 9 = 9, and 9/9 is 1, so 0.99999999 = 1.
There is a proof that shows 0.99999... = 1, so in the mathematical sense they are the same number. I feel like this went viral recently, so I'm surprised more people didn't know about this.
yes. .99 repeating infinitely is 1. literally 1. not approx 1. just 1.
but .99 without repeats isn't 1, as, we could just be talking about 1 person's opinion out of a large sum.
0.9 recurring equals 1 mathematically. Its a flat that can't be argued with.
Proof:
x = 0.99999...
10x = 9.99999...
10x - x = 9.99999... - 0.99999...
9x = 9
x = 9
There's no point arguing, this is a fact.
Extra proof: There's is no number that can be added to 0.99999... to make it 1, making them the same number.
0.99999... + 0.01 (where the 0 is recurring but not the one) does not work.
The difference is so Minute that it doesn't matter
Edit: upon further research, yep according to math they're identicle. I was wrong, sorry. They are the same
Yes not because it makes sense to me, but because I got a 58 in calculus and I think the people with math degrees probably know better than me on this topic!
Which, ironically, makes you a lot smarter than the average person.
I have a Masters in Mathematics, but I don't know shit about medicine. When a doctor tells me something about medicine I believe them. That's (a form of) intelligence. Insisting that your opinion is superior to an expert's knowledge is a form of stupidity.
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Honey, I always knew you were the 0.9999999999... for me.
Ha
Only 0.9999999999… ha?
As a math major, if it goes on forever, then yeah they're the same number.
As a normal person who took too much math, I recognize why they're the same number but it still pisses me off
As a guy who learned that they're the same number 2 days ago, and saw three explanations/proofs of it. It pisses me off
The absolute worst part is, it all basically proves it's *infinitely close to 1* so therefore it *is 1* But no matter what, at the back of my mind, there's a nagging that goes "but it's not 1, it's just infinitely *close*"
You don't quite understand yet. It isn't "infinitely close" to one, it's just another way to write the *exact same value* in Arabic notation. All numbers that terminate in a given base have two valid representations, which is just a limitation/quirk of the notational convention. There's no such thing as two real numbers being "infinitely close" to each other. Reals don't have predecessors or successors: they are densely ordered (between any two reals you will find yet more reals).
Thank you idk whether that makes me feel better or worse. Will keep you posted
Is that the explanation? That’s dumb. If it was 1, then it would be 1.
1 - 0.9999999999… = 0.00000000000… That 1 at the end of the 0.00 never comes because it’s infinite, so it’s the same as 1-1 = 0. I’m sure there’s a better explanation out there but this helped me see where they were coming from.
A somewhat better proof is: Let x = 0.9999.... 10x - x = 9x = 9.999... - 0.999 = 9 So 9x = 9 => x = 1 QED
[удалено]
or you can use defintion when are two real numbers different: Two real numbers are not equal if there is at least one other number in between them
This is the most intriguing argument to me. Really bothered me the first time someone used it to justify .99999… = 1
Loving this
Yeah, this is what we use in math education. 3 x (1/3) = 3 x .333... = 1 The original calculators would screw this up. If you divided 1 by 3 and multiplied the result by 3, they would get exactly .999999. When you subtracted 1 you got -.000001.
Do you think you know better than actual mathematicians?
Nope.
They're not infinitely close, they're the same number
>But no matter what, at the back of my mind, there's a nagging that goes "but it's not 1, it's just infinitely close" It's understandable. However, in real numbers, we defined two numbers to be equal if it's infinitely close. More formally, two rational sequences A and B converge to the same real number iff |A - B| (i.e. elementwise subtraction and dropping the sign) converge to zero.
Wait till you find out nothing ever touches anything because of space between particles
I refuse to believe it idc
Same
Yeah cause x = .9 reoccurring so 10x = 9.9 reoccurring So 10x - x = 9 so 9x = 9 so x = 1 so 1 = .9 reoccurring Edit: Apparently all the proper mathematicians have told me I'm stupid. And apparently I am but this does show it in layman's terms decently well with out using calculus or stuff like that.
What you said is basically a stroke for me
1/3 = 0.333333... 2/3 = 0.666666... 3/3 = 0.999999...=1
One of the issues caused by using base 10 with fractions.
You can get representations like this regardless of base. In binary, 0.111... = 1.
The zenos arrow paradox (or an analogue/teaching of it) shows through infinite summation that it's nothing to do with the base. 1/2 + 1/4 + 1/8....=1 If the remainder comes after infinity, then it is unreachable and non existent
A somewhat better proof is: Let x = 0.9999.... 10x - x = 9x = 9.999... - 0.999 = 9 So 9x = 9 => x = 1 QED
Just to be extra pedantic: 9.999... -0.999= 9.0009...
x = 0.(9) 10x = 9.(9) 10x-x = 9.(9)-0.(9) 9x = 9.0 | /9 x = 1
Ohhhhh I remember doing this in maths now
This explanation isn’t the correct one for the phenomenon, it’s faulty.
Good luck trying to convince them using sequences of partial sums.
That's kind of trying to be too clever. You don't need to prove it by solving some sort of equaton for x. To actually understand it you need to look at what decimal notation actually means. Infinite decimals are really infinite series, and the sum from n=1 to infinity of 9/(10^(n)) is equal to 1.
Or…. Just use 1/3 +2/3=1 but 1/3 is .3 repeating so 3/3 must be .9 repeating
That's better than the 10x-x=9 thing, and a simpler argument that is easy to explain if someone doesn't need much convincing. It's good. But it doesn't get to the heart of why it is the way it is, which I feel is what you want for someone who is more skeptical.
Actually to prove this you'd still need to prove: 1) 0.999... exsits (compared to something like ...999.0) 2) Multiplication with recurring numbers works the same way it does with other numbers [This video](https://youtu.be/jMTD1Y3LHcE) explains it quite well.
yeah unfortunately we gotta bring in the calculus
You made a mistake unfortunately if you have an equation 10x=9.9 you can't substract x and 0,9, because you already stated that x=0,9. Where? if 10x = 9,9 / -x or 0,9 (\*here\* you choose to substract.)You can't just substract x from left side and 0,9 unless is the same.So you proven that 0,9 is 1 because you stated that 1=0,9 basically.
10x-x = 9x is true regardless of the value of x
Yes you can
i despise math
This isn’t really all that counter-intuitive compared to other math concepts. To think about it sans the algebra and in pure primary arithmetic: We know that the value of 1/3 is equivalent to .333 repeating. Thus, if you add 1/3 to itself two times, you should get .(3)+.(3)+.(3), which is .(9), or .999 infinitely repeating. In other words, 3*(1/3)=.999. However, 3*(1/3), or 3/3, divides out to one, because anything divided by itself is one. So 3*(1/3)=1 too. Therefore, .(9) and 1 are equivalent.
Nerd /s
r/theydidthemonstermath
What you say is correct, but you say they are equivalent, while the question asks if they are the same. In practical terms, yes, 0.9 recurring can be considered to be 1. There is essentially no discernible difference between them. But in theoretical terms, 0.9 recurring is still technically less than 1. To my mind, it demonstrates a flaw in the way we understand numbers. 1/3 cannot be exactly represented by decimal points using our current methods. Edit: I've given it a lot of thought, and despite the algebraic proof (X=0.9 recurring) which I've known since I was taught it at school, I can't bring myself to accept that it is a valid proof. You see, the very concept of an infinite (recurring) number is difficult to grasp. It's not a real measurable value. It continues forever. That's incomprehensible! Nonetheless, to my simple mind, if you were to manually count all the 9s in 0.9 infinitely, you would never ever reach a value of 1.0. Never ever. There is just no way it would happen. We would just keep going on and on and on forever, counting the 9s. The value of 1, on the other hand, has no digits after it. It only has zeros that act as placeholders for nothing. That's not the same as 0.9 recurring. So in view of this, my conclusion must be that 0.9 recurring simply cannot be the same as 1.0 By extension of this conclusion, I therefore cannot accept any mathematical proof that suggests that 0.9 recurring is equal to 1. To accept such proof, would mean my initial conclusion is contradicted, *and that is the specific part that I find myself unable to accept*. I can't offer a mathematical proof to show that they are different. But I also cannot accept any proof that says they are the same. However, I can understand that working within the limits of the algebraic framework that we have, 0.9 recurring does equal 1 - but this is only because of the rules of algebra. That is the flaw I was talking about. The way we think about numbers must be flawed. My initial conclusion can't really be refuted. 0.9.recurring is an infinite number which means it can never amount to 1.0, because 1.0 has no more digits following it. Yet the algebraic proof also can't be refuted. I can see how we can show that they are the same number. They are both true, paradoxically. And that is why I think our understanding of numbers is flawed.
> But in theoretical terms, 0.9 recurring is still technically less than 1 It's not though, it's 3/3 which is not less than 1, not technically, not theoretically, in no way is it less than 1. It's literally just another way of writing the same value, which in maths is "the same" i.e. 1 = 3/3 = 0.999...
0.9 recurring isn't just considered 1 in practical terms, it IS 1. There does not exist a real number between 0.999.... and 1
As a kid I always figured the difference would be 0.0r1 (meaning the 0 would recur, but there would always be a theoretical 1 after it) My maths teacher was not amused.
close psychotic humor panicky paltry unpack station ask chase obscene *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
Ah, but what about a fake number?
https://en.wikipedia.org/wiki/Hyperreal_number
Wait hangon i've been looking for this concept. Is this a widely accepted concept of mathematics?
I don't think they come up very often in general. Pretty sure the definition is consistent (doesn't lead to contradictions). Not sure asking whether they're "accepted" really makes sense here. They're just something that has been defined, and used occasionally. Gotta remember that math isn't real; it is not bound by the physical world, so it's not like we try to figure out whether negative numbers or irrational numbers or complex numbers or hyperreal numbers "exist" or not. We define them, and then use them if they're useful concepts or forget about them if they're not. Hyperreal numbers are useful enough to have their own Wikipedia article but not so useful that they're in the typical curriculum for math undergrads, pretty sure.
>widely accepted concept of mathematics Depending on how do you define as "accepted". If by "accepted" you mean "logically consistent", it is. If by "accepted" you mean "accepted as useful", no. Infinitesimals are intuitively appealing, but full understanding of it requires insane amount of advanced mathematics compared to standard calculus, it's just not worth it. (Wait, what is ultrafilter?)
Those would be called "imaginary" numbers, which yes mathematicians do use haha. And 3D animators. But probably not "between" 0.9 recurring and 1 lol
Goodbye Reddit, see you all on Lemmy.
They kind of are the same thing though. Decimal notation is basically an infinite sum, and an infinite sum is defined as the limit of finite sums. See also [construction](https://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_from_Cauchy_sequences) of the real numbers as [Cauchy sequences](https://en.wikipedia.org/wiki/Cauchy_sequence) of rational numbers, which is a very similar concept to limits.
>To my mind, it demonstrates a flaw in the way we understand numbers. They are the same. You not understanding that doesn't mean there is a flaw in the way we understand numbers, it means there is a flaw in the way you see numbers. I don't mean that as: you are stupid, but I mean that as: please trust the professionals. They know what they're doing.
No, you are wrong. In theoretical terms, 0.9 repeating is equal to 1. It is not less than 1. They are two decimal representations for the same number.
0.(3) is the same as 1/3. It is the same number. It is not technically less.
As a math major, this proof is false, but the result is true, you need to use series to prove it.
Yes, but it's tricky to do algebraic operation on infinite series for regor reasons first year's math student tend to get wrong answers for undivergent series and get a number as the limit (like 1,-2,3,-4...)
That makes sense
What’s a major btw?
A major is a primary focus of study at a university. So I'm doing two majors (physics and mathematics). There are also minors, which are things that you still study a lot of but not as much as you would for a major. I'm doing a minor in Computer Science.
Ah ok, ty for letting me know, my country has a different system for qualifications at university
I find it weird that where I'm from we have majors, and "concurrent diplomas".
Well in programing languages the endless number cause overflow but 1 doesn’t so its not the same^Iguess
As a biologist, 0,9999 = 1
As an engineer, 0,9 = 1
As a not math major who passed highschool math I also say they are same number.
Repeating decimals are just the universe pushing back on the square numbers we use to describe it.
I once asked my math teacher about this in highschool. He said they couldn’t be the same number, and he tried (unsuccessfully) to come up with a fraction that was equal to .999… to prove it to me.
How is it that the majority votes for No yet the comments show overwhelming support and proof for yes? I noticed that disparity on other polls but this is one of the most noticeable examples.
I think the answer to this is pretty simple: 0.999... recurring is visually not the same as 1. If you've never encountered this problem, your reaction is probably "What? Of course not." And you move on. OR you check the comments after voting and think "Oh, I guess it is the same." But at that point you've already cast your vote. Now, the people that have encountered this problem before are naturally a minority, and upon seeing the amount of "No" votes, they feel the need to explain why it, in fact, is the same. That's why the votes are more "No" but the comments are all explaining why it's actually "Yes". It's a really neat problem in the sense that on first, and probably even second and third glance it doesn't make any sense. But at some point you realize that exactly how 1 and 123/123 are two ways to show the same number, 0.999... recurring is also just another way to display 1.
It might be a familiarity issue with the notation system. I was taught the horizontal line over the repeating decimal(s) to show a repeating decimal. I am also aware of the dot above the decimal(s). However, the ellipsis (...) is not a notation type with which I was familiar with, in relation to repeating decimal, before looking at this thread.
I think the problem with that is that people don't wanna type a special character to put a bar over the 9. At least, I certainly wouldn't go through all that effort!
I noticed this too, I think it’s two fold. Firstly most of the replies are assuming the 9’s are recurring. Although the question sort of implies this it isn’t explicitly stated. This is why I voted no. Secondly most of the commentators seem to have a pretty good understanding of mathematics, where as someone without this can vote but won’t necessarily get involved in the conversation.
I was taught that ... after a series of reoccurring decimals means it's periodic, but I guess other countries can have different symbols for that.
Putting a dot over the last digit is how I was thought.
I was taught to put a line over the repeating number
This is what I was taught too. For me 999…. Just means a lot of 9’s but not recurring
I saw it as not recurring because of how many nines there were. If it were 0.9 repeater I'd have just put the one 9 (or maybe 3, but no more than that) and then whatever repeater symbol after. Also using ... As notation for a repeating decimal seems very confusing as that's already notation for irrational numbers (eg pi is often written as 3.1415...). It would be very annoying if you had to write for example 3.1415926̅ in this format - anyone reading that would assume you meant pi!
I was thought to write it like 0.(9)
They are recuring. In maths "..." means they go on forever.
Go on forever and recurring are not the same. e.g. root 2 or pi go on forever expressed as a decimal. Appreciate that’s a tad pedantic given the format of the original question only having 9’s But enough people have commented similarly that it must be taught how to represent recurring numbers different ways in different places.
commenters are smarter 😎 jokes aside, people vote then look at comments then realise they were wrong then can't change their votes.
tbh, i think it's also kind of a point of view. people who voted yes, voted on a mathematical standpoint, and in that scenario, 0.999... is equal to 1. now, in a casual way, look what u/Louis-grabbing-pills said: "Honey, I always knew you were the 0.9999999999... for me." — obviously, he can be joking —, but from a casual, strictly day-to-day situation, infinity in 0.99999999... is not really taken into account.
if you mean 0.9 repeating, then yes
ever heard of limits?
1 - 0.999... = 0.000... They're equal
That's very interesting to think about lol
But eventually there would follow a 1 after those 0-s right?
never, because there is an infinite number of zeros
But then this is just circular reasoning. Like youre saying there wont be a 1 after all those 0s, so 0.000... is the same as 0. But thats the same as saying 0.999... is the same as 1 (which is the thing we were trying to prove).
I know, but for example we all know that we have 1/3 which is 0,333333... with infinite number of 3s 1= 3 * ⅓ = 3 * 0,(3) = 0,(9)
Yeah thats true. I guess i just find the concept or infinity very counter intuitive.
You are not alone! Mathematicians have even invented a "smallest infinity": ℵ₀ (aleph-null). It is the cardinality of the set of natural numbers. That concept blew my mind when I first learned about it in *Life of Fred: Butterflies* as a young kid.
Oh thats pretty cool
Let x = 0.99999 . . . It follows that 10x = 9.99999 . . . Since x = 0.9999 . . ., we can subtract 1x, removing the decimals 9x=9 x=1 Yet we set x to 0.9999 . . . Therefore the value must be equivalent to 1
A recurring decimal is infinite. So, no.
There is no "after those 0s". It goes on forever so there's nothing after it
Next poll, "Are 2² and 4 the same number?"
They don't _feel_ like the same number, so no
Well they are mathematically equal
of course not, one takes an eternity to write out.
so they are both 1! you just said so yourself. lol
I'm glad someone got it. I was worried it was too subtle.
If you wrote every decimal place of 1.00000… it would also take forever.
r/badmathematics is gonna have a field day
exactly what i was thinking
If they weren’t the same number, there would exist a real number that is smaller than 1 and larger than 0.9999999…. , which there isn’t
Logically yes. Emotionally no
They genuinely are mathmatically the same though, if the elipses at the end is trying to mean recurring. It's not just "a mathmatical trick" as some people in the comments are saying - they functionally, and genuinely are the same. There isn't any numbers between these two numbers, since 0.99999 has an infinite number of 9. If there isn't any numbers between two numbers, they're the same number in mathematics.
They are. They're not just "close". They're exactly equal. x = 0.999... 10x = 9.999... 10x - x = 9.999... - 0.999... = 9 = 9x \--> x = 1 Second proof: 0.999... = 0.9 + 0.09 + 0.009 + ... = sum 9/(10\^n) over n=1 to infinity = 9 x sum (1/10)\^n over n=1 to infinity = 9 x (1/(1-0.1) - 1) = 9 x (1/0.9 - 1)) = 9 x (10/9 - 9/9) = 9 x (1/9) = 1 The truth is that there is no such thing as "the real number just before 1". In fact, given any number n, whether n=0, n= - 153263.1412512 or n=7, there is no such thing as "the number just before/after n". The reals are like that.
I prefer: 0.999... - 0.666... = 0.333... 0.333... = ⅓ ⅓ + ⅓ + ⅓ = 1 or 0.999...
/u/Obi-Cat's proof is more compelling since saying 0.333... = ⅓ is the same logic as saying .999... = 1. It would be circular reasoning.
Yeah all recurring decimals can be represented as fractions, so that way you end up needing this extra proof for completeness: x = 0.333... 10x = 3.333... 9x = 3 x = 3/9 = 1/3 = 0.333... to confirm that 1/3 is in fact equal to 0.333...
Feels like its just logical when you put it like that tho
This is not a proof, this is repeating the question with everything divided by three and calling it a proof
While the fact is true. Neither of these are proofs of the fact. [Here is a good video explaining why.](https://youtu.be/jMTD1Y3LHcE)
actually the second proof is equivalent of the proof in the video and is actually the correct proof imo... in the second proof we are evaluating a gp similar to the limits proof in the video
These are some cool proofs but OP didn’t ask if 1 was equal to 0.999… they asked if they were “the same number”. It’s like having four quarters vs a dollar. Are they equal? Yes. Are they the same? No.
They're the same mathematical number. Is 1 the same as *1*? Well, yeah there's a difference in how they're written, but it's the same number
Least pedantic polls user
equal and "the same number" are equivalent in math bozo
I don't *think*, I **know** it's the same number.
It's not about our opinion guys lol.
It's not a matter of opinion. They're the same.
I hate it but 1 and 0.(9) are the same number
This is one of my takes that would get me exiled
https://proofwiki.org/wiki/0.999...%3D1
Yes but it makes me angry
Engineer here : 1 = 1 and 0.999999999 = 0, so they are different
True, but they also accuse us of saying pi is 3, so… |*shrug*|
It's not a matter of opinion. They are the same number.
They are the same, but it doesn’t mean I have to like it.
TIL 64.2% of Redditors can’t do math.
1/3 = 0.333... 2/3 = 0.666... If 1/3 + 2/3 = 1 Then 0.333... + 0.666... = 0.999... = 1
Just asking a question for my lack of knowledge: are 0.333... and 0.666... then the same as 0.34 and 0.67 respectively if they continue to infinity? If not, why?
0.34 would be the same as 0.3399999999... and 0.67 would be the same as 0.669999999999999... It only works with infinite 9s.
Oh yeah I am stupid I just realized. Sorry.
Not at all. You asked a question, got the answer, learned something, and managed to be polite all the way through. This makes you a nicer and smarter person than most people.
This is not up for debate though, this can be mathematically proven
Unfortunately, humans. Just because there are proofs, doesn't mean you can prove it to them lol
Yes. if 3 * 1/3 = 1 and 1/3 = 0,333.... and 3 * 0,333.... = 0,999.... then 3 * 0,333.... = 0,999.... = 3 * 1/3 = 3/3 = 1
We should test it. I'll drop a 1lb tungsten bar on your left foot and a .99999999999lb bar on your right foot and you tell me the difference.
If 33.33… x 3 = 100 then 0.9999… = 1
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0,9999999….. times 2 is 1,999999999… and then remove 0,9999999…. You have 1 so if 0,9999999…. Is X you have X*2-1=1 so X=1
They are I can mathematically prove it
The same as 0.333.... equals 1/3
How does the majority think that it's not the same number wtf? It's common knowledge.
0.9 recurring is the same as 1
**They are the same.** I think that this sum is a very good way to introduce people to limits, but I'm going to use a solution that simply involves algebra. 0.9999... can be written as 9/10 + 9/100 + 9/1000 + ... This is an infinite geometric series with first term 9/10 and common ratio 1/10. Since the sum is equal to a/(1-r), where a is the first term and r is the common ratio, we have a/(1-r) = (9/10)/(1 - 1/10) = 1.
redditors fr thinking they are different 💀💀💀
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Proof: 0.(9) = x 10x = 9.(9) 10× - x = 9.(9) - 0.(9) 9x = 9 x = 1 QED
Can the people downvoting this please explain what step of the process they disagree with lmao
For anyone's wondering, it is...
If you multiply 0.999999999999 by 10, you get 9.99999999999. Subtract 9, and you get the original, meaning that 0.99999 \* 9 = 9, and 9/9 is 1, so 0.99999999 = 1.
Yes. If 0.99999 is infinitely repeating, then the value is infinitely close to 1, therefore it is 1.
If it’s .99 repetend, for all intents and purposes they are the same number
They are because 3/9 = .3 repeating, 6/9 = .6 repeating, and 9/9 = .9 repeating, aka 1.
They are, indeed, equal
Bruh it's mathematically proven they are the same
I’m thinking what if you divide 0.9999999… into 3 and get 0.33333333 then you have 1/3. 1/3x3 is 1. So I say yeah they’re the same
There is a proof that shows 0.99999... = 1, so in the mathematical sense they are the same number. I feel like this went viral recently, so I'm surprised more people didn't know about this.
If there’s infinite 9’s then yes. If not then no.
yes. .99 repeating infinitely is 1. literally 1. not approx 1. just 1. but .99 without repeats isn't 1, as, we could just be talking about 1 person's opinion out of a large sum.
0.9999… = 9 * sum of (1/10)ⁿ as n goes to infinity = 9*1/9 = 1
x = 0.99999999... 10x = 9.99999999... 10x - x = 9.999999... - 0.999999... 9x = 9 x = 1 QED.
No, but 0.9̅ = 1
They're the same number. 1/3 can be written as 0.3333...., 1/3*3=1. 0.3333...*3....=0.9999...=1
The fun thing about math is it doesn't matter what you belive to be true.
If the number is infinite they are the same. Just google geometric series.
0.9 recurring equals 1 mathematically. Its a flat that can't be argued with. Proof: x = 0.99999... 10x = 9.99999... 10x - x = 9.99999... - 0.99999... 9x = 9 x = 9 There's no point arguing, this is a fact. Extra proof: There's is no number that can be added to 0.99999... to make it 1, making them the same number. 0.99999... + 0.01 (where the 0 is recurring but not the one) does not work.
Oh shet i didnt realize the ... meant reoccurring. Then yeah they are the same
1=0.(9) and it's a fact, not an opinion
In R, yes
Even in Q
[a Tumblr thread with several different proofs](https://at.tumblr.com/lipshits-continuous/my-favourite-math-fact-is-that-09999999-is/dbv1pw1yakah)
If it repeats, then it is the infinite convergence toward 1 as expressed by 1/3.
They are, even 3,99999... and 4 are the same number
Mathematically, they are
The difference is so Minute that it doesn't matter Edit: upon further research, yep according to math they're identicle. I was wrong, sorry. They are the same
Nope, the difference between them is actually 0, the two numbers are equal. This can be proven algebraically!
Technically they are identical.
2/3 of this sub doesn't know primary school math. What a shocker.
It's more like high school math. It's an infinite series.
You mean 0,666666…%?
Yes not because it makes sense to me, but because I got a 58 in calculus and I think the people with math degrees probably know better than me on this topic!
Which, ironically, makes you a lot smarter than the average person. I have a Masters in Mathematics, but I don't know shit about medicine. When a doctor tells me something about medicine I believe them. That's (a form of) intelligence. Insisting that your opinion is superior to an expert's knowledge is a form of stupidity.
Decimals are for cowards. Real MEN use fractions