>Pluto is not a planet
>tomato is a fruit not a vegetable
>0.99999 = 1
>>28892193
I agree with all of those
>>28892193
>>Pluto is not a planet
>>tomato is a fruit not a vegetable
>scientists are neckbeard losers
All of those are correct, not sure about the 0.99
>>28892193
0.99999 isnt equal to 1
0.infinite 9's is
>>28892798
The easiest proof:
1/3 + 1/3 + 1/3 = 1
0.33333.. + 0.33333.. + 0.333333.. = 0.99999.. = 1
The other proof
0.9999.. = x
10x = 9.9999999..
10x - x = 9.99999.. - 0.999999.. = 9
10x - x = 9x
9x=9
x = 1
There are also geometric series proofs.
>>28892193
>series of arbitrary distinctions
Okay, OP
When it comes to taxation, like sales tax, .99 is ultimately 1. So .99 = 1
>>28893053
Sales tax isn't 1/99th, though.
>>28893000
Math proves itself to not be perfect
>>28894111
that's not true though
the field of real analysis makes certain that everything is consistent and clearly defined
calculus I/II/III can get a little wonky without the rigorous proofs to build it upon, but any serious mathematics holds water at every corner
>>28894195
>the field of real analysis makes certain that everything is consistent and clearly defined
1/3 + 1/3 + 1/3 = 1
yet
0.33333.. + 0.33333.. + 0.333333.. = 0.99999.. = 1
m8
>.999x10=9.99
>9.99-.999=8.991
Dipshit
>>28894256
what the fuck are you trying to demonstrate
0.3333.. isn't a valid mathematical construct and you can't operate on it, or equate it to anything in any meaningful way
the best you can do is define it as the infinite series of 3 * 10 ^ -n from n = 1 to infinity (more precisely, the limit as m goes to infinity of n = 1 to n = m). if you add three of these series together, you just get the infinite series 9*10^-n from n = 1 to infinity, which is a geometric series, whose limit is equal to one because any given x > 0, one can choose a y such that 1-y < x
all you're doing is pulling shit out of your ass, and then wondering why it smells like shit
>>28894436
>0.3333.. isn't a valid mathematical construct and you can't operate on it, or equate it to anything in any meaningful way
yes you can you faggot. just because a construction isn't finite doesn't make it 'not a mathematical construct'. fractions are dedekind cuts but you're not bitching about them
>>28894517
real numbers* are dedekind cuts i mean
>>28892193
>tomato is a fruit not a vegetable
It bears seeds. That makes it a fruit.
>>28894563
vegetable is a culinary and not scientific classification. it's both
>>28894517
i'm not talking about the number 1/3, i'm talking about 0.33333..
1/3 is a real number that is rigorously defined
0.33333.. is high school notation that is meaningless gibberish, and you need a geometric series to talk about it meaningfully
>>28894573
>vegetable is a culinary and not scientific classification. it's both
Come on now.
>>28894584
.333... is the real number that is higher than any .333...3332 and lower than any .333...3334. It's a perfectly coherent thing to talk about, you're just being a pedant when you're not even technically right.
>>28894674
real analysis is about being technically right, at the cost of being pedantic, which is what i'm doing.
get fucked.
>>28894584
Please explain why you have such a massive stick up your ass about repeating decimals. It's just notation. What's the big fucking deal?
>>28894674
The point of a repeating decimal is that there is no last digit. I'm not that guy by the way. I have no problem with repeating decimals.
>>28894711
you're not being technically right. you're declaring your version of fractions to be some retarded platonic ideal and pretending equivalent alternatives don't exist despite the fact that they do and real numbers expressed as (possibly infinite) sequences of numbers generated by the division algorithm are one of them.
>>28894674
for any given .333...3332 and .333...3334, the number .333...33321 falls between both
you need limits to get where you're trying to go
>>28894745
i didn't say there was a last digit. .333...333 (actually you don't need the 2 at the end though it doesn't break anything) and .333...3334 are all undeniable rational numbers for any number of threes you stick in them. .333... means the unique real number which is greater than .333...333 for any number of 3s and less than .333...334 for any number of 3s.
>>28894787
i said that. the real number is greater than .333...333 for any number of threes and less than .333...334 for any number of threes.
>>28894746
>real numbers expressed as infinite sequences of numbers generated by the division algorithm are one of them
you've backed yourself into a corner here, because that's exactly what i've been arguing this whole time. geometric series are a sum of numbers generated by the division algorithm
.33333.. doesn't have a mathematical backing to support it because "tack a 3 on the end of the decimal" isn't a valid operation. "add 3 divided by 10 to the nth power" is, however, and that's how geometric series are generated
>>28894812
>.333... means the unique real number which is greater than .333...333 for any number of 3s and less than .333...334 for any number of 3s.
That's a shitty definition, because it includes more than just .3 repeating. Infinitely more numbers in fact.
The pedant's definition here >>28894436 is what I think of implicitly with .3 repeating. He says it smells like shit, I say it doesn't.
>>28894838
are you implying that there isn't a number of the form .333...33321 that is greater than any number of .333...3332 and smaller than .333...3334?
every single pair of numbers of the form .333..3332 and .333..3334 have a number .333.33321 that lies between them
that isn't a good enough definition of 1/3
>redditors legitimately believe that .99999...=1
>>28894842
>because "tack a 3 on the end of the decimal" isn't a valid operation
add a three to the end of a finite sequence sequence is an operation. not that this is relevant.
you can also describe this as a geometric series, yes. i'm not sure why you think that means it's incoherent
>>28894882
No it doesn't. .333...333 and .333...334 get arbitrarily close to .333...
>>28894883
i'm implying that you're switching quantifiers around my definition without realizing it.
exists unique X st forall n .3...3 (n places) < X, .3...34 (n places) > X
>>28894991
0.333...333 and 0.333...334 are terminating decimals. The dots don't mean the same thing in the case of 0.333...
>there are people in May 2016 too stupid to understand that 0.999 repeating equals 1
>>28895046
how do you define "n places" without a geometric series?
>>28892798
That image is triggering me.
>>28895085
Real numbers can be defined as an infinite set of rational numbers. That's basically what I'm doing.
>>28895095
least n such that (whatever number)/((1/10)^n) is an integer
and again it's also fine to use a geometric series. why do you think it's incoherent, did a geometric series kill your mother? the geometric series are even finite in this case if that's what was bothering you.
>>28895139
Sticking a 4 on the end conflicts with your use of ". . ." to mean an infinite number of 3's.
You're contradicting yourself. It's like saying infinity plus one.
>>28895207
what the hell are you talking about? i'm writing .333...333 to mean any finite number of threes and .333...334 to mean any finite number of threes followed by a four. these are rational numbers and since they converge i can use them to define a real number.
>>28893000
But .999999999... doesn't equal one. It is just an infinite number that is infinitely close to one. I can divide the number one by the number two an infinite amount of times without it becoming zero. e.g., I can fit an infinite amount of infinitely thin lines between two lines. As such, I can add an infinite amount of decimals getting increasingly smaller in increments of x/10 to a given number without it ever reaching the next whole integer.
As for in real life, I would disagree too. I would argue, even though this is a specific subject I'm ignorant on, infinite values don't exist.
https://www.youtube.com/watch?v=ffUnNaQTfZE
You do realise that neither 1/3 or 0.333... aren't real right? They're just concepts invented to cover a certain amount of x. Because 0.999... and 1 are different concepts, 0.999... cannot equal 1, and anyone who tries to prove it is working in a fundamentally flawed direction.
>>28895265
OK, If they terminate, then they do not get "arbitrarily close" to 1/3, and there will always be an infinite number of closer numbers, and your definition
>.333... means the unique real number which is greater than .333...333 for any number of 3s and less than .333...334 for any number of 3s.
still sucks.
>>28895310
>Because 0.999... and 1 are different concepts
which are provably equivalent in a common framework. sure you can imagine a framework in which this is not the case but that's presumably not what people are talking about.
>>28895331
are you trolling? i have an infinite amount of these rational numbers, not just two of them. that's the point of how i ordered my quantifiers
There exists a unique x such that (For all n ...). The x is defined such that it holds this property for any .333...333, .333...334, not just a fixed pair
>0.999... = 1
its like saying 999/1000 = 1000/1000 = 1 or 99.99999...% = 100%
it's wrong, but math can still "prove it right"
That's what i meant when i said "math proves itself wrong", its meant to be logical but its not, and that's my favorite thing about it.
>>28895278
but yes, you fucking retard, .99999.... is exactly equal to one
this isn't up for debate
>>28895278
>he doesn't understand infinity
le xD epic trole
>>28895310
1 isn't real either. it is a concept invented to cover a certain amount of x
1.00000... is not that different of a concept
>>28895608
>its like saying 999/1000 = 1000/1000 = 1
But it's not, because there's a difference between .999 and .999... One's finite, the other repeats infinitely
>>28895423
No, I wasn't trolling. I misread your initial post >>28894674, and this post >>28894991 reinforced my thought that you were using the incoherent idea of two repeating decimals with last digits.
I wasn't following the other thread, where you gave a more precise definition here >>28895046
Though I do feel foolish now looking back on the other thread, you did change the wording from "any" to "all". If I'd looked at that post, it would've clicked for me that you were talking about a set.
>>28895864
>999.99.../1000 = 1000/1000
jenius, simpli jenius
>>28895780
".99999..." comes with the implication that the number is infinite. It is a decimal in the tenths place with every following part of the number (e.g. hundredths, thousandths, etc.) being the preceding number divided by ten. As in .9/10=.09, .09/10=.009, so on and so forth. This means that the following decimal place is getting infinitely and infinitely smaller. A number that is expanding at an infinite speeds, but expanding infinitely and exponentially slower. Just as (1/2)/2)/2)/2)/2)2)2)2)/2)/2)/2)/2)/2)/2...) will never equal 0 (as it contracts at an infinitely slower rate), .9+.09+.009+.009... will go on forever and will never be able to reach 1.
However, this is one man's opinion and I do believe mathematics is very much open to interpretation. If there is any way you can disprove infinite division, I am 100% willing to change my opinion. Well, more like 99.999...% percent willing, but it's all the same anyhow.
>>28892914
>0.9999~ repeating is 1
What
No it isn't
It infinitely approaches but never reaches one
If anything, the only thing that gives it a hard definition it is that it ISN'T one
You're so wrong m8
>>28896234
Just let the poor idiot believes what he wants to.
>>28892193
0.999... is equal to 1 because there's nothing between an infinite number of 9s in the decimal place and 1 therefore they are the same number.
>>28892798
thank u melanie
>>28893000
Anyone can use algebra to prove that 1 = 2. The numbers are not the same, therefore they're not the same. That's it.
>>28896299
The "proof" that 1=2 is flawed though. It looks like it's real but there's a point where it does something that's not possible to do in math even though it looks like you can.
>>28896247
There is a difference. It's 0.0000...1, progressing as infinitely as the 0.9999... itself progresses
>>28896379
The point of the "dot, dot, dot" is that there is no end; 0.9999... is inifinte. There is no "last" digit. So the "there's always a difference" argument betrays a lack of understanding of the infinite. Someone already showed a proof earlier in the thread.Oh wait, I forgot, a random guy on /r9k/ knows more about math than every mathematician that agrees this is fact.
>>28896425
I didn't say that there was a last digit. I only said that a difference exists.
>relying on ethos so heavily
topkek, speak for yourself when you choose to speak
>>28893000
Here's the geometric series proof.
>>28893053
That actually is quite untrue. You pay for something that costs .99 with a dollar, you will get a penny back.
The original citation should say 0.999999(infinite 9s) = 1.0 which is true. They left off the "infinate" part.
>>28896425
It's as I said earlier, 0.9 infinitely repeating is very much equivalent to 1 when it comes to most practical applications, but it is defined by the very fact that it isn't 1. You can map out 0.9 to the quadrillionth digit and more, and it still will be less than 1.
You can feasibly round it, but you're still rounding it and not representing its true quantity.
>>28893000
>Does use ...-math like a barbarian to deceive people
>Mentions a geometric proof
>Doesn't mention it's a limit thing, to further deceive people
You would make a great muslim.
>>28896542
>You can map out 0.9 to the quadrillionth digit and more, and it still will be less than 1.
Ok, but 0.9 to the quadrillionth digit isn't 0.9(repeating). You can't "map out" 0.9(repeating) because it has no end. Again you fail to comprehend infinity.
>>28893000
if 0.99999...= 1 then wouldn't ....000001 equal zero?
if ...00001 equals zero than couldn't you add onto it infinitely and have it still be zero?
but surely ...00001 plus itself one time equals ...000002
an infinite number of times and then it becomes infinite
in which case infinity would equal zero
>>28892193
>0.99999 = 1
Nice touch, very subtle desu not many people would associate that with the fedora as it should be
>>28896566
>and more
My point is, you can increase the resolution of your measurement of 0.9 infinitely repeating as much as you want, infinitely, even, and every time it will be less than one. You are failing to comprehend me, if anything.
It does not magically become 1 at any point in time.
>>28896200
I've always heard it explained as, if two numbers are different from one another,then you can name a number that lies in between the two
because you cannot identify a number that lies between .999 repeating and 1, the two are one and the same
>>28896569
>but surely ...00001 plus itself one time equals ...000002
>an infinite number of times and then it becomes infinite
No, an infinite number of time multiplying it by itself would still result in ...0000(infinity), which is still 0. You guys really can't comprehend infinity. The ... never goes away. There will always be an infinite number of zeroes before the number.
>>28896591
There's no such thing as mapping out an infinite number of times. Your logic is flawed. Every time you map another 9 there's still another 9 after it. Again, you don't understand infinity.
>>28896617
No, you're the one who doesn't understand infinity, because you're trying so hard to assign a finite number (1) to a number that isn't finite.
You're still not understanding me at all.
>>28896591
So which step are the proofs that have been posted wrong?
>>28896604
yeah but the amount of disappearing zeros also never goes away.
also aren't there an infinite number of zeros before real numbers anyway? ...0000001.000000000,,,,
>>28896637
The "...". It's a retarded way to describe real numbers and not proof safe.
>>28896653
>yeah but the amount of disappearing zeros also never goes away.
There's always an infinite number of zeroes before any nonzero though. It's still infinitely close to 0 no matter what.
>also aren't there an infinite number of zeros before real numbers anyway? ...0000001.000000000,,,,
Yes, but they have no bearing on anything because there's no non-zeroes before the first set of infinite zeroes or after the second set of infinite zeroes.
>>28896680
How else do you want to describe an infinitely repeating number?
>mfw people argue against mathematical truth
https://en.wikipedia.org/wiki/0.999...
>>28896695
With limits or infinite sums for example. But if you use these you can't deceive people in thinking "0.99999..." is 1.
>>28896712
>mathematical truth
true in math =/= true irl
math is not perfect, now phisics in the other hand...
>>28896712
>>28896695
Note how the Wikipedia article speaks about "converging"? That's not the same as being equal to.
>>28895278
0.999.... is by standard definition the limit of the sequence 0.9, 0.99, 0.999,.. (which is 1), it's not an infinite sequence in itself it merely denotes the limit of one. This is a consequence of defining infinite decimal expansions as infinite sums, which are limits.
>>28896751
>In other words, the symbols "0.999..." and "1" represent the same number
0.999 = 1
subtract .999
0=.001
multiply by 1000
0=1
>checkmate number fags
>>28896777
Shouldn't this be described as an asterisk after the statement then? Seems to be misleading, since I'm not very knowledgable in the subject, it feels like I'm being mislead.
>>28896712
>mathematical truths
>true
pick one
>>28896742
This is the dumbest post I've ever seen on 4chan
Math is how we model what happens in the real world. Believe it or get fucked
>>28896684
i'm trying but that really explains nothing at all.
would not .000001 + ...000001 equal ...00002?
and if not then why does .....00001.00000... +.....0001.000000... equal ...00002.00000.....?
>>28896247
Imagine I have two pieces of paper. One being having a surface area of .999 units repeating (even though this is impossible to imagine in the confines of this dimension and all others below it) and one having a surface area of 1 unit.
If I take the one unit piece of paper, and cut it in half an infinite amount of times, and arrange the paper so that the first two pieces are one unit way from each other, and every following piece is half of the distance of the preceding piece is from its preceding pair (i.e. 1 unit, 1/2 units, 1/4 units, 1/8 units, etc.) I will have an infinitely smaller and smaller gap. That is to say, a gap that cannot be filled and a piece of paper that cannot be cut a finite amount of times. So rather that there being nothing between an infinite and a finite, there is an infinite amount of continuously, instantly contracting space within a infinitely small amount of time.
Now imagine you have a piece of paper with a surface area of .999 repeating that, instead of continuously and instantly contracting, it is continuously and instantly expanding. Imagine it "starts" at a length of .9 and expands by the value of the preceding number divided by ten, which is to say repeating 9's. Since it is expanding by a number that is dividing itself, it the amount that it "grows" gets infinitely and instantly smaller.
While this means that the difference in surface area between the two pieces of paper is growing infinitely and instantly smaller, the rate at which it does is growing infinitely and instantly slower. Henceforth, the two pieces of paper will never reach the same surface area.
(IN MY HUMBLE OPINION)
>>28896593
I still have no feasible way of imagining how infinite numbers could fill a finite space. There is no possible way you could make a triangle with sides of 1, 1, and .999 repeating. If we lived in a dimension wherein infinite units of area or length could exist, this shape would still be physical impossible as far as I know.
>>28896816
It's much pretty playing on people's lack of knowledge of mathematical semantics. It's a simple truth about the way we represent numbers and isn't really profound in any way.
>>28896777
ok cool, but what if we are actually talking about an infinite sequence of 9s starting after the decimal point?
>>28896909
>There is no possible way you could make a triangle with sides of 1, 1, and .999 repeating.
Right here friendo
>>28896825
>Believe it or get fucked
reddit af
so you saying 99.999...% = 100%?
and that 99.999.../100 = 100/100 ? Try arguing that with your teacher
you confounding math with physics you dummy
>>28897561
>triangle
i think hes talking about a Perfect Triangle, forgot the name
>>28897668
Pretty sure if your grade was actually 99.999...% you would be able to argue your way into getting a 100%. Especially if it was a math professor.
>>28897561
But .999 repeating is an infinite number between 0 and 1. How can you have the lines intercept if there is an infinite about of space between finite and infinite numbers?
>>28897775
.999 is equivalent to 1.
haha oh wow i am laffing
>>28897668
see >>28896503
>all these faggots arguing about 0.999... = 1
Yes, 99.999.../100 = 100/100. This is highschool level math that you should have done, at the latest, your fucking junior year.
This isn't even really a fucking math debate, it's a fucking epistemological one. Due to the very fact that it's infinite, it's unknowable. If it's unknowable, it's irrelevant.
The fact of the matter is that it is impossible to show through any mathematical means that .999... =/= 1. If it's impossible to show a distinction, they're the same.
>inb4 some faggot does something with a calculator that shows 0.awholebunchofnines =/= 1
>>28897811
>1-.000...1=.999...
>.999...+.000...1=1
>1+.000...1=1.000...1
???
>>28897950
You can't have an infinite (keyword: infinite) series of zeros followed by a one like that. Because, you know, it's infinite and shit.
>>28898008
>infinite numbers can't become finite
woah it's almost like that means .999... can't become 1 holy shit my nig
>>28898085
No, it's because like .999...=1, .000...1=0
>>28898085
No, it's almost like 0.000...01 isn't a valid number. It's what's called an infinitesimal, and it hasn't been used by serious mathematics for 400 fucking years, you dipshit.
0.999..., on the other hand, is something that can be constructed with real mathematics. See >>28896503
Please go back to your high school and ask your calc teacher why he gave up on you. Failing that, consider suicide.
>>28892193
People who say
>"I don't care what nobody says"
are there seriously people who still refuse to accept that .999 repeating is 1?
jesus christ come back after finishing high school
>>28898235
See I just replaced nobody with anybody as I read it. Reading a second time made me see what I just did.
>>28898235
People who say
>"I could care less"
>>28898258
I once met a woman who tried to justify it as, "I will care even less if you don't stop now."
>>28897911
please get out of reddit and get a math book that isn't from fucking middleschool
are you american?
>>28898190
>>28898166
>copy-pasting and screen shotting from math websites
Yes, because everything on the internet is true. If .999 repeating is really 1, then how come e.99999999 repeating =/= mc^2-.99999?
>>28898362
Well the stuff I posted that was on the internet was also from a conversation I've had with the head of the math department at my university.
>>28898310
>what is a geometric series
>>28898362I like your style, anon.
>>28898417
>university prof instantly equals correctness
They have fucking gender studies professors at most universities nowadays to.
god your a faggot
>>28898429
>comparing the head of the math department to a gender studies professor
>your a faggot
ok
>>28898362
First, let's get that notation corrected.
(0.999...)e =?= mc^(2-(0.9999...))
Now, if we replace 0.999... with 1, we get...
(1)e =?= mc^(2-(1))
Which equals...
e =/= mc^(1)
And that's not correct.
Nice b8, tho. You got >>28898457 good.
>>28898501
fug, I said e =/= mc^(1) was wrong. Whoops, should been
e =?= mc^(1)
And that's incorrect
>>28898501
>nice b8 tho
i think you mean 'b&', and no, im not underage you fucking tryhard
>>28898457
>woah mathematics is a totally established thing that has never been tampered with and mathematics professionals have never been wrong about anything
>It's what's called an infinitesimal, and it hasn't been used by serious mathematics for 400 fucking years
woah i guess mathematicians can be wrong with those logics, so i guess your just a fucking dum bass!
>>28893000
that just prove you should take into account rounding error
not that 0.999=1
1 = 0.333 + 0.333 + 0.334
but lmao maths XDDD
>>28898798
You round 0.03 to 0.1? Are you autistic?
This isn't even the only proof. See >>28896503 for the geometric series proof.
but lmao maths XDDD
>>28895819
If 1 isn't real then what's this? Checkmate faggot.
>>28898428
>>what is a geometric series
comfirmed american
