Debate.
The stories and information posted here are artistic works of fiction and falsehood.
Only a fool would take anything posted here as fact.
Only a fool would take anything posted here as fact.
Debate.
>>768484819
Well ,if they're not the same number, then there must be a number between them ,right? So what number is between them?
>>768485122
>>768484819
To be fair, there is a difference, but since humans don’t work with infinite numbers (we don’t like/use them on that scale) you could argue that it is the same number. Its just that on an infinite level, there is a difference, it doesn’t really affect us
1/3 = 0.33333333333333...
3*1/3 = 3*0.333333333333...
3/3 = 0.9999999999999999...
1 = 0.99999999999...
>>768484819
>Debate
Don't tell me what to do
>>768484819
0.9 repeating doesn't really exist. It's a function of digital processes/processors trying to recreate an analog function like 1/3, or 3/3.
You can treat 1/3 (or pi for that matter) as an endless string of digits, or you can save space, time, and sanity by expressing them as functions of a whole, such as one being divided in three, or a circle's circumference being divided by its diameter.
The process that makes 0.9 repeating doesn't really exist, so the result it gives - 0.999 etc.- expressed as the result of a multiple of three divided by itself is 1.
>>768487447
I guess there are other Asians on this board.
>>768485122
There isn’t one!!!
I submit that .333 continuing doesn't actually equal 1/3. It just infinitely approaches 1/3 in the same way .999 continuing doesn't equal 1 and just approaches 1 infinitely. By definition for the 9 to repeat forever it cannot be 1.
>>768484819
looks good to me
ITT: what is convergence?
"When the runner crossed the distance to the turtle, the turtle will always have moved ahead in the time it took to reach it. The runner can never reach the turtle." - Everyone not agreeing with the equivalency in OP
close enough
>>768488103
For fucks sake.
Set x = 0.999...
Multiply both sides by 10
10x = 9.999...
Subtract x from both sides (x from left, convert x to 0.999... on right)
9x = 9
x = 1
Simple proof. It's not a matter of argument or opinion.
>>768485122
This logic doesn't follow. If I'm standing next to my friend in a line, your reasoning would state that since there's no one in between us, we must be the same person.
>>768485474
You can't multiply a recurring number dipshit.
If it's recurring, it's still unexpressed. The recurring is an approximation, it's actual value can't be written in base ten.
Pretending that it can is flawed and leads to mistakes like your post
>>768488103
Ding ding ding. Winner
>>768485347
/thread
>>768489941
False equivalency. These numbers exist on a defined spectrum where there position is defined directly by their value. Not at all true for physical objects like humans.
>>768484819
It cannot be, because the infinite series of "0.999..." still does not bring it to exactly "1.0" following any known mathematical formulation. Only queers and retards believe that they are truly equiv. to one another. But, hey, for retards "close enough is good enough" right?
>>768489873
This isn't a proof because if you multiply 0.999.. by ten, you don't get 9.999..., you have one less digit.
So let's rewrite it:
x = 0.999..99
10x = 9.999..90
10x - x = 8.999..01
So it's infinity minus 1 digits, which when taken away means you have 9-0.00....9 = 8.999...1
Infinity either exists as a number (which means infinity minus 1 isn't the same as infinity) or else it doesn't (in which case you can't times infinity by ten or apply any functions to it). Either way your proof is conceptually flawed
>>768490305
>These numbers exist on a defined spectrum where there position is defined directly by their value
What part of that means that two numbers with nothing in between are the same number?
Let me put it logically for you.
There is a theoretical number next to 1 with no numbers in between. There is a number next to this number and so on and so on.
If these numbers are the same, then by going through an infinite amount of numbers, we'd reach 2 and end up with 1=2
>>768490407
You are apparently operating with maths rules that no one else uses. Check any source, multiplying .999... by 10 does in fact result in 9.999...
you cannot get 0.99999...
change my mind
>>768490551
>what is argumentation
I never said the original argument was correct. However your initial response was also flawed.
>>768490407
>x = 0.999..99
But that's not the same number, genius. You literally just redefined the equation so that it does not involve a recurring number.
>>768490660
Proof required.
(High school maths guides don't count as proofs)
>>768489873
Correct by definition. Nothing more to discuss.
>>768490856
Can you read? Either infinity is a number (behaves like a number) or it isn't/doesn't
>>768490660
He's operating under the premise that the infinitely repeating series must have a final digit. If that is true, then shifting the decimal point to the right will in fact mean there is one digit less, ergo he is right. If it is not true, then the number will repeat infinitely and can never be expressed, therefore it can never be operated on, ergo he is right.
>>768490706
>>768490377
>>768488103
>>768485347
Achilles and the tortoise. American education level is literally 500 BC.
>>768490856
Exactly, because you cannot do math on a recurring number. Either you have to follow the number until it stops recurring (if it does), or you have to take a segment of that number and accept a certain amount of error. You cannot do normal functions on infinity.
> ITT art and lit types arguing math
1 - 0.9999... = 0.0000 = 0 in the limit. If it's an infinite sequence, then they are literally equal.
>>768490997
>therefore it can never be operated on,
Is it easier to just make stuff up instead of receiving an education?
>>768491179
The inability to operate on numbers that haven't been expressed isn't made up.
>>768490886
>I don't have any defense for my nonsense so im going to shift the burden of proof
Ok.
>>768489941
As the distance between you closes, you become the same person.
If you are occupying the same space as your friend to the nearest angstrom, you likely now share organs, fluids, etc.
Please do not try to occupy the same space as your friend. It's going to be uncomfortable at best.
Actually every body 0.9999... is not the same as 1 because it is a complex quaternion therefore it has arrived by different processes so it is a different number.
>>768484819
There's nothing to debate. These are two ways of writing the same number, once simply, and once as the sum of an infinate series.
>>768491274
They've both made separate claims at this point, and the burden of proof is on both of them.
>>768484819
Infinite repeats are irrational numbers. Trying to express them as rational numbers is about as intelligent as the "can God make an X so big that he can't Y" crap. /thread
>>768491274
I responded with a proof, you replied saying that's not how numbers work. I asked for a proof since you made a claim. Please stop acting like a retard
I agree
>>768491516
3x0.9=2.7
3x0.99=2.97
3x0.999=2.997
3x0.9999=2.9997
etc etc
It never reaches 1 or even 0.9 recurring, the last digit is always 7
>>768491344
this https://en.wikipedia.org/wiki/Quaternion
>>768491516
This is just an issue with comparing base 3 to base 10. It doesn't prove anything.
>>768491344
>>768491654
Explain this to me like I'm an idiot
>>768490377
It usually stems more from the reason for 0.999... being there in the first place. If it's 3/3, then it is 1.
If it's just some orphaned, repeating number, defined by it's infinitesimal proximity to 1 - so, if you cannot put a number between them, no matter how small - then as long as it isn't defined by not being 1, it essentially is.
If its definition is being asymptotic to 1, then while it may come infinitely close, it cannot be 1.
For the first case, even your calculator will show you 1.
>>768491508
I see it, I just want to try it on people.
>>768491648
Absolute retard
>>768484819
There is no more point debating this, than there is debating those crackpot "flat-earth" delusions, square-root of minus one, or that tediously recurring grade 4 arithmetic ( is the answer 9 or is it 1 ) problem, or anything else vaguely similar that seems to provide endless amusement to your average low-IQ b/tard trolls.
>>768491952
but i is surprisingly useful for something that doesn't exist.
>>768490004
Omegalul, high school maths cucks who got an A and think they are sick are funny af. Currently in my fourth year of theoretical physics at uni and i can mathematically prove your statement wrong in at least five different ways. Just stfu and acknowledge that because you have heard of a matrix doesnt mean you know shit about number theory
>>768485122
1/∞
>>768492078
>"You're stupid and wrong and I can definitely prove it! I just don't want to..."
>>768492078
I hope you actually talk like this.
>>768491952
>square-root of minus one
What's there to debate about this?
>>768492175
You aight white boi
>>768492200
it doesn't actually exist?
Imaginary numbers are fun
>>768492342
Alright, here's a question, what does it mean for a number to exist?
>>768484819
Only if you want it to.
>>768492421
It has to be portrayable to exist as part of the real subset.
i, as part of the imaginary subset, is only portrayed as a result or a symbol.
>>768491729
Because all physical existence can be defined as mathematics many things can be defined as a number in an equation and when a number is in an equation it changes so therefore when a numbers changes it has a definition that definition is what is known as a quaternion so a quaterion is a number value throughout time that changes so when you compare two numbers that are in different states or representations they are not considered the same because entropy is taken into play in representation in calculus. therefore 0.9999... is not the same as 1 in an equation over time.
>>768484819
Easy
1/9 = 0.11111...
2/9 = 0.2222...
3/9 = 0.3333...
.
.
.
8/9 = 0.8888...
so 9/9 = 0.9999... and at the same time 9/9 = 1
BSc in Pure Maths, Msc in Applied Maths, PhD in Mathematical Epidemiology here. They're equal.
The reasons why have already been explained in this thread.
>>768492634
This is right.
>>768492670
This is literally just a shortcoming of the decimal system. Try it in base 3 where nothing in the equation has to repeat:
1/9 = 0.01
2/9 = 0.02
3/9 = 0.10
.
.
.
8/9 = 0.22
So 9/9 = 1, and at the same time literally nothing else.
The problem is that the system you are using is not divisible by 9 or 3. Use a system that is and the problem goes away, because there is no problem.
>>768490551
>There is a theoretical number next to 1 with no numbers in between.
No there isn't? There's an infinite amount of smaller numbers closer to 1.
>>768493588
Yes there is. If you work backwards from 1 using the smallest possible distance between the two, the very first number you would come to would be that theoretical number.
>>768493574
I used my explanation during math finals and they accepted it.
>>768484819
1-0.99999999999=0.0000000000001
>>768494252
Probably because it's the most widely used explanation for a highly advanced mathematical concept and for the most part it suffices. In my third grade class I said that Christopher Columbus discovered America and they accepted that too.
>>768493760
What is the "smallest possible distance between the two"? A defining feature of the real numbers is that there is always a number between two other numbers. Assuming you have two distinct real numbers x and y, you can always construct a number which is between them, for example (x+y)/2.
>>768484819
in some situations, yes
>>768494658
That is a defining feature of real numbers. We are talking about a theoretical number which doesn't actually exist. It's a concept that has no realization.
