Is 0.999... exactly equal to 1?

[Anonymous No.5896730]

Last thread degenerated into discussion on animal emotions. Here is the improved , step-by-step version of the counterproof
1:: 1=0.999...
source: http://en.wikipedia.org/wiki/0.999......
academic consensus: nearly all academics agree
proofs: Many

2:: 1-0.999...=0
If two numbers are exactly equal their difference is zero x=y x-y=x-x=0

3:: 1-0.9-0.09-0.009-...=0
The difference can be described as process of sequential subtraction from 1

4:: ((1-0.9)-0.09)-0.009-...=0
Each step can be reliably described as...

5:: (((1/10)-0.09=1/100)-0.009=1/1000)-...=0
equivalent to division by 10 at each step of the process

6:: (1-0.9=1/10-0.09=1/100-0.009=...)=0
the sequence is obviously based on division by 10 which is...

7:: 1/10/10/10/10...=0
a repeated division by tens which can be defined as...

8:: 1/(10*10*10...)=0
division by a infinite sequence representing all divisors combined x/a/b/c=x/(a*b*c)

9:: (1/(10*10*10...))*(10*10*10...)=0*(10*10*10...)
but we can cancel out the combined divisors from both sides! x/y=z x=z*y

10:: 1=0*(10*10*10...)
Canceling the left side is trivial (x/y)*y=x

11:: 1=0*10*10*10*...
the right side can be examined as a sequence with zero at start which leads to

12:: 1=(((0*10=0)*10=0)*10=0)*...
propagation of zeroes to the right and since 10*0=0 at any step, that means:

13:: 1=0
reductio ad absurdum, but wait there is more

14:: x*1=(x*0=0) since x=y z*x=z*y
every number is zero.

[mtp !EKFQOBEsKo No.5896748]

1/(10^n) tends to zero as n tends to infinity, similarly sum from n=1 to infinity of 9/(10^n) tends to 1

cant be bothered to read your retarted proof, but saying that (1/10^n)=0 as n gets arbitarly large implies 1=0*n is just idiotic

[Anonymous No.5896806]

I have question, what is consequence of 1 not equal to 0.999...? is it just a insignificant technicality or it affects some kind of cornerstone of math?
It seems to me that 0.999...=1 is not that important and really unintuitive. Can math just stop using it to avoid the problem? People would trusts math more.

[mtp !EKFQOBEsKo No.5896809]

>>5896806
not sure if serious, http://en.wikipedia.org/wiki/0.999......

[Anonymous No.5896842]

>>5896809
I think it proves my point, its just a convention.
We can move to better number system and resolve the problem once and for all.
Some quotes from the article.
Timothy Gowers argues in Mathematics: A Very Short Introduction that the resulting identity 0.999... = 1 is a convention as well:

However, it is by no means an arbitrary convention, because not adopting it forces one either to invent strange new objects or to abandon some of the familiar rules of arithmetic.[47]


Jose Benardete in his book Infinity: An essay in metaphysics argues that some natural pre-mathematical intuitions cannot be expressed if one is limited to an overly restrictive number system:

The intelligibility of the continuum has been found—many times over—to require that the domain of real numbers be enlarged to include infinitesimals. This enlarged domain may be styled the domain of continuum numbers. It will now be evident that .9999... does not equal 1 but falls infinitesimally short of it. I think that .9999... should indeed be admitted as a number ... though not as a real number.[55]
The intelligibility of the continuum has been found—many times over—to require that the domain of real numbers be enlarged to include infinitesimals. This enlarged domain may be styled the domain of continuum numbers. It will now be evident that .9999... does not equal 1 but falls infinitesimally short of it. I think that .9999... should indeed be admitted as a number ... though not as a real number.

[Anonymous No.5896854]

>>5896842
>natural pre-mathematical intuitions
It's probably better to let a rigorously defined mathematical system like the real numbers decide if such natural intuitions are valid/necessary. Natural intuitions are in general not to be trusted. Rational thought is wonderful at weeding out the good ones from the bad.

[Anonymous No.5896959]

>>5896730
SOMEONE FINALLY FUCKING UNDERSTANDS AN IOTA OF BASE TEN! GIVE THIS FUCKING MAN A MEDAL!

[Anonymous No.5897775]

there is something illogical at 0.999...=1
I mean is 1 is rational number, than 0.999... must be too, but it a real.

[Protocat No.5897807]

>>5896730
For your step 7, surly 1/10/10/10/10/10... e.c.t tends towards zero but will never actully reach it, and you are basically rounding down voiding the proof. Zero in this case is 'untouchable'.

[Anonymous No.5897813]

yo retards. vhart, that chick from youtube has a video of this shit. the cunt knows her shit so enough with the potatoes.

[Anonymous No.5897820]

[Anonymous No.5897828]

>>5896730
you have in step 8 that 0=0
Then in step 9 you multiply both sides by infinity which is invalid as a step and conclude that 0*infinity is zero on the right hand side but 0*infinity is 1 on the left hand side.

[Anonymous No.5898796]

0.99999...
= 9(0.11111...)
=9(1/9)
=9/9
=1

[Anonymous No.5898813]

>>5898796
You assume 1/9=0.111... which is actually incomplete division. Its like claiming 1=0.999... because 0.999...=1(hint: its the same class of numbers, and you can't assume one to circular logic around the other)

[Anonymous No.5898818]

>>5896730
>proofs: Many
all wrong

[Anonymous No.5898821]

>>5897828
Its a sequence which has an infinity as limit
this exact same sequence is cancelled from left.
(x/(seq))*(seq)=x isn't it obvious?
Now the right side, the sequence is evaluated per step, and we can clearly see that at ANY STEP the value is 10*0=0 ZERO. Nice "Zero infinity" you have here. The sequence evaluates to zero and the amount of its members does nothing: the multiplication by zero is like dominos falling toward the right, collapsing the "infinity" to 0.

[Anonymous No.5898852]

>>5896730
nice! you have combined the 1 != 0.999... troll and the divide subtly by 0 and get 0 = 1 troll into one! have a muffin.

now someone just has to combine this with the 9/3(1+2) troll and we are golden.

[Anonymous No.5898907]

There is no division by zero. >>5898852
Where did you find one?

[Anonymous No.5898964]

>>5897820
Oh, that retarded image. I cringe every time any self-righteous "defender of math" brings it up.
1.
x = 0.999...
10x = 9.999... (wrong multiplication by 10 leaves a final 0)
10x - x = 9.999... - 0.999...(actually 9.999...000... which is LESS than 9.999...)
9x = 9 (actually 8.999...10...)
x = 1
0.999... = 1
counter example for N=5
x=0.99999
10x=9.99990
10x-x=9.99990-0.99999
9x=8.99991
x=0.99999, now each time you increase N the difference DOES NOT disappear it just goes further to right.

2.second "proof" since 1/3=0.333... 0.999...=1 but 0.333... is an approximation of 1/3 and its circular logic: 1/3=0.333... relies on 1=0.999... (its the same class of numbers)

3. third "proof" the proper formula for geometric series is a*((1-(r^m))/(1-r)) not (a*r)/(1-r)
read http://en.wikipedia.org/wiki/Geometric_series#Formula
You using the reduced formula which computes a limit where r^m is discarded, not the sum.
now if you bring cauchy sequences and dedekind cuts ,these rely on real number system postulates which have the archimedean property that relies on 1=0.999... being correct. Nice try though. "bask in glory of being retarded"

[Anonymous No.5898980]

>>5896730
1. not a step
2. correct. But .9999=1 is the same equality as 1+1=2.
3. Incorrect, on the left you have a series, on the right you have a number. You cannot do this, what you need to write is:
Limit as n->infinity for Sn, where Sn=Sn-1 - 9/10^n, S0=1.

Everything that follows even if correct is irrelevant as a flaw is already made.

For the step that looks dodgy step 9, when you include the limit function, it is obvious why it is wrong.

[Anonymous No.5899010]

>>5898980
Umm, that's what the infinite series is, idiot.

The problem is we "don't know" what inf/inf is. This is the "problem" with OPs proof. (Look at: lim a->inf a/a=1)

But it's about time we introduce infinite decimals and accept them.

For example the definition of e:
lim n->inf (1+1/n)^n =e
but using the rule that 1/inf=0 we see that
lim n->inf(1+0)^n!=1
and
lim n->inf 1^n=1

which are clearly contradictions.

As such, we need inf decimals to end this debate.

(By the way, why do we say "approaches" or "arbitrary close" if 0.999...=1?

[Anonymous No.5899017]

>>5898980
1. any step, does not matter which result in difference: infinite steps don't magically erase it.
2."But .9999=1 is the same equality as 1+1=2."
Than why you need a proof if its that obvious?
Do you see that 0.999... is not an integer like 1?
3. Limit is not a sum. Its an bound which != sum
The formula i provided is sum formula.
The step 9 is just cancelling the divisor: if you can't cancel a divisor by multiplying you can't use math at all.

[Anonymous No.5899027]

>>5898980
Umm, that's what the infinite series is, idiot.

The problem is we "don't know" what inf/inf is. This is the "problem" with OPs proof. (Look at: lim a->inf a/a=1)

But it's about time we introduce infinite decimals and accept them.

For example the definition of e:
lim n->inf (1+1/n)^n =e
but using the rule that 1/inf=0 we see that
lim n->inf(1+0)^n!=1
and
lim n->inf 1^n=1

which are clearly contradictions.

As such, we need inf decimals to end this debate.

(By the way, why do we say "approaches" or "arbitrary close" if 0.999...=1?

[Anonymous No.5899538]

>>5898813
Divide 1 by 9 and see what you get.

[Anonymous No.5899542]

>>5898964
So what DOES paste taste like? I only ask because you seem to have eaten a lot of it.

[Anonymous No.5899554]

>>5899542
I don't know about paste; I've never tried it. Pasta, on the other hand is my favorite disk.

[Anonymous No.5899731]

>>5899538
I get 1/9. 0.111.. is approximation of process of division. the decimal representation of 1/9 is incomplete by design, just like decimal representation of pi.

[Anonymous No.5899890]

>>5899731
Incorrect. Pi is a nonrepeating decimal. 0.1111... is a repeating decimal. That means that it continues forever. As in, forever forever. As in, it never ends, and there is no hidden 0 or 5 or whatever at the end, because it doesn't have an end. It is an absolutely perfect representation of 1/9, just as .9999... is an absolutely perfect representation of 9/9, or 1. It is NOT infinitesimally off.
But what do I know? I only have a degree in this crap.

[Anonymous No.5899893]

>>5899890
Clarification. Pi also continues forever, but with no discernible pattern.

[Anonymous No.5899915]

>>5899890
I don't dispute that 0.111... contains only 1's
I dispute the idea that 1/9=0.111...
"It is an absolutely perfect representation of 1/9"(retarded bullshit: only 1/9 is perfect representation of 1/9)
1/9>0.111.... since the division never completes.

[Anonymous No.5899921]

>>5899893
But if the pattern is random/not discernible, why we can
1.calculate as many digits of pi as we want?
2.calculate any digit without calculating the rest?
if there was no pattern you can only guess the outcome. PI has a pattern and there are infinite series that converge to pi.

[Anonymous No.5899958]

>>5899915
The division completes just fine; it's just that YOU can't complete it. Because there can only ever be 9s, you know with perfect clarity and absolute authority what the value of the number is at all points and levels of accuracy.
>>5899921
The problem here is that while you could generate an *arbitrarily* accurate depiction of pi, you cannot ever produce an *absolutely* accurate representation of it. No matter how fast your computer is, or how long you leave it on, there will always be digits you do not know, unlike .9999..., which is uniform throughout its entirety.
It's like this, if you have a straight line of infinite length, you will always know what direction it is going. The same can be said for a curving line that follows a known pattern. If, however, you have an infinite line that wiggles about unpredictably, you can follow it as far as you like and find out what way it is going, but you can never know the direction it is pointing at ALL points to infinity.
A clumsy analogy, I know, but I hope it illustrates the difference.

[Anonymous No.5899969]

>>5899958
"The division completes just fine"
Then write out the decimal result without any ...
You can't: the division NEVER completes.
>"YOU can't complete it."
No one else can. Math doesn't have an exception for my person. Its either true for everyone or not.
>"cannot ever produce an *absolutely* accurate representation of it."
Same thing with 1/9 , dumbass. 0.111... is never absolutely accurate, its always one step behind 1/9.

[Anonymous No.5900010]

Infinitists are getting too butthurt to reply.
Good job OP.

[Anonymous No.5900008]

>>5899010
You can't use " inf/inf", because it is not a number. You can only examine it's properties through limits or other methods.

>For example the definition of e:
That is not a contradiction.
>but using the rule that 1/inf=0 we see that
that is not a true rule, the limit as n->inf of 1/n = 0, you cannot use inf as a number.
In undergrad math we don't say the limit part, because it is understood that this is what is meant, but you are missing this understanding. It is clear that you don't understand it because you are trying to sum in a limit result into the center of a limit.

>(By the way, why do we say "approaches" or "arbitrary close" if 0.999...=1?
'we' shouldn't because that is incorrect.
Saying that .9999=1 because the difference is infinitesimal is right for the wrong reasons, there is no little .0000...001 bit that is missing. It is exactly equal.


>>5899017
1. is just stating definitions, it is bad convention to call it a step.
2. In the sense that they are exactly equal, there is no 'they approach the same value' it means that they are the same equality as 1=1 or 2=2.
3. That is the problem, you are using false rules.
9. You are trying to use rules that are specific for simple algebraic, and generalising them (to series, which may not be true). This shows that you didn't read what was written, what was said is that by doing this dodgy step in step 3, you will get false conclusions. You are saying "haha you are dumb if i start with this (bullshit that is not valid), then I can do this logical step and now maths is false, I am so smut"

[Anonymous No.5900012]

>>5899969
>Same thing with 1/9 , dumbass. 0.111... is never absolutely accurate, its always one step behind 1/9.
No it is not. The problem here is that you are counting in base 10. If you count in base 9:
1/9=0.1
1/9*9=0.1*9=1, there is no 0.00..001.

[Anonymous No.5900033]

>>5900008
The a countable infinite series, not "inf"(infinity is not some magical object immune from the rules of math)
The thing is, if can calculate the limit/sum why you can't use operations on it?
If "inf" is exact same as "inf" inf/inf=1. The series doesn't magically evolve into uncountable vague mess which cannot be described or operated on.
Series divided by itself gives 1.
Next:
>but using the rule that 1/inf=0 we see that
There is no such rule. The example is series that approaches infinity. You don't understand the process:
(1/(series))=0 false conclusion from 1=0.999...
(1/(series))/series=0*series Left side cancels
1=0*series (since people can't understand direct x*0=0) 0 is multiplied by first member of series giving 0, then its applied to the next member, etc
giving the result(any member of series must be multiplied by the previous member which is 10*0=0, at no point the series reaches any other value than 0):
1=0 (reductio ad absurdum )

next:
> It is exactly equal.
Its disproven by the counterproof. Read it again.
Next
1. Its step 1, assuming the premise that 1=0.999... (which i disprove by reductio ad absurdum)
2. you cannot define them exactly equal without proof. This "argument" is bullshit.
Its like saying 3.5=4 because its like 1+1=2
0.999... isn't an integer. 1 is an integer.
3.> generalising them (to series, which may not be true).
Is series some object which does not obey laws of math? Are you trying to say infinite series deserve special rights?
1-0.999...=1-0.9-0.09-0.009-...
don't make "dodgy step in step 3" any less valid
for retards who cannot comprehend the "dodgy step 3":
1-0.999...=0
0.999... is equal to series 0.9+0.09+0.009+... with ratio 1/10. Do you dispute this?
Now:
1- series=0 Do you dispute this?
representing the series
1-(0.9+0.09+0.009+...)=0 DO you dispute this?
removing the brackets
1-0.9-0.09-0.009...=0 We're back to "dodgy step 3",?

[Anonymous No.5900034]

>>5900012
In base pi, pi=1, but thats not "absolutely accurate" thats defined a "one pi".
You example is retarded. base 9 means any number with 9 as divisor just moves its decimal point to left once, not representing 1/10 but defined as "1/9" in base 9 0.1(1/10) is 1/9 BY .DEFINITION. its like proving 1=0.999... by DEFINING 1=0.999..., welcome to circular logic.

[Anonymous No.5900039]

>>5900034
*correction base pi is pi=10 one pi is 10
(pi/10 however is one)

[Anonymous No.5900044]

OP is sure getting emotional. His little proof has no supporters and filled with holes.
*inb4 the entire OPs "proof" is deconstructed by someone with math Phd lurking here*

[Anonymous No.5900046]

>You will never create a truely random number

[Anonymous No.5900059]

>>5900033
>>5900033
>Are you trying to say infinite series deserve special rights?
Yes they do, because we can get strange conclusions if the diverge or converge. In finite series, we can simply just use what is required (such as the last term or the sumo 0f the terms), in infinite series we can get things like for any term above n, it is larger than d, where you choose the d beforehand (ie. it is infinite). That is why you work in limits of series, a thing that you constantly forget, I recommend relearning cauchy series, and epsilon proofs (linear algebra and calculus).

>If "inf" is exact same as "inf" inf/inf=1.
This is not necessarily true, which appears to be the problem in your proof. Depending on the infinity type, they may be different order. We can get things like inf1/inf2=inf3, inf1/inf2=0, or even inf1/inf2^2=inf3.

>(1/(series))=0 false conclusion from 1=0.999...
This is false, it is:
the limit as n-> of 1/Sn=0. It is important to keep the limit so later on, you do not multiply with limits (as there are sometimes different rules).

So let's look at this properly, the limit as n->infinity will be called 'lim n' for brevity

1/lim nSn=0
1/lim nSn*lim mSm = 0*lim mSm (I assume you mean times not divide. Also seperating the variables)
and here is the problem, on the right side. This is why we need to keep the limits it.
>0*infinity=0,
this is false, 0*infinity=R (some real number). This is because infinity is not a real number so it has different properties than a real number.
When you try to seperate it into a non limit you get problems.

>at no point the series reaches any other value than 0
Once again you need to revisit limits. By this logic, lim n 1/n can't equal 0 because at no point does this series reach zero.

>"dodgy step 3"
(on the idea of 'dodgy') the dodgy part is not the mathematical logic, the dodgy part is that you are assuming the properties of limits and series are the same, and hence using them interchangably. They are not.

[Anonymous No.5900073]

>>5900059
>get strange conclusions if the diverge or converge.
If they(series) diverge we get infinities if they converges we get something below a finite limit, but limit doesn't mean a sum: Its an upper bound. Nothing strange. Infinite summation formula you use is flawed and should not be used for convergence since its incomplete. I don't calculate any limits in the proof, i calculate series sums.
next:
> Depending on the infinity type, they may be different order
Its the EXACT SAME SERIES.
0.9+0.09+0.09+... and 0.9+0.09+0.09+...
Its logical that if we operate on EXACT SAME SERIES we get the EXACT SAME RESULT on either side. Its like arguing that 1!=1 because its a "different type of 1"

>(1/(series))=0 false conclusion from 1=0.999...
>This is false, it is:
I don't operate with limits, period. I operate with series and their sums/products. Keep you limits to yourself.
>at no point the series reaches any other value than 0
>Once again you need to revisit limits. By this logic, lim n 1/n can't equal 0 because at no point does this series reach zero.
1/n cannot be zero for ANY n. Whats your point?
> the dodgy part is that you are assuming the properties of limits and series are the same,
I don't USE ANY LIMITS. If you find any equation where i have written the term "lim"(excluding quotation) i will send you a thousand bitcoins.

[Anonymous No.5900106]

OP are you a finitist?

[Anonymous No.5900107]

>>5900073
>If they(series) diverge we get infinities
Nope. Some series are bounded but diverge.

[Anonymous No.5900109]

>>5900073
The series 1 + (-1) + 1 + (-1) + ... diverges but is not infinite.

[Anonymous No.5900120]

>>5900109
>The series 1 + (-1) + 1 + (-1) + ... diverges but is not infinite.
Looks like it converges to either 0 or 1. Its dependent on numbers of members N
if N is odd the series sum is 1
if N is even the sum is 0

[Anonymous No.5900123]

>>5900120
You obviously don't know what "converges" means, in the context of infinite series.

[Anonymous No.5900124]

>>5900120
To be convergent a series must have only 1 limit, not oscillate between two or more.

[Anonymous No.5900133]

>>5900106
I don't subscribe to any labels such a "finitism", math should not be a religion/ideology. However if you like to know where i stand on math philosophy , my views are that:
I don't hold (all forms of) higher math in high regard and unless it can be derived from primitives and those primitives are proved to be absolutely correct, it should not be used.
I believe math should obey the laws of logic and that common sense/intuition should have a priority over formalism/axioms/forced abstractions.

[Anonymous No.5900138]

>>5900073
>Its logical that if we operate on EXACT SAME SERIES we get the EXACT SAME RESULT on either side. Its like arguing that 1!=1 because its a "different type of 1"
'Order' means order of magnitude. This is 1st year undergraduate maths. Also you are opperating on non-similar series, one side is a limit*. The other isn't.

>I don't operate with limits, period. I operate with series and their sums/products. Keep you limits to yourself.
>Once again you need to revisit limits. By this logic, lim n 1/n can't equal 0 because at no point does this series reach zero.
> the dodgy part is that you are assuming the properties of limits and series are the same,
Exactly that is the point. you are using properties that only limits have, while not using limits hence the 'applying properties to series that only limits have'.

This level of analysis requires skills and tools beyond your current. When I use limits I could generalise it to not limits then prove that it is a limit but you should have learn limits.

*Since after mentioning it many times you still don't understand I will say it again. You say 1/infinity=0 it is not true, only 1/n as n-> infinity=0. That is a limit.

>I don't USE ANY LIMITS. If you find any equation where i have written the term "lim"(excluding quotation) i will send you a thousand bitcoins.
I hope your job doesn't involve abstract math, because you must suck at it.

Relearn Linear algebra and calculus. You are missing the understanding of limits.

[Anonymous No.5900140]

>>5900133
>I believe math should obey the laws of logic and that common sense/intuition should have a priority over formalism/axioms/forced abstractions.
This is an oxymoron. No wonder you are confused.

[Anonymous No.5900142]

>>5900133
>I don't hold (all forms of) higher math in high regard and unless it can be derived from primitives and those primitives are proved to be absolutely correct, it should not be used.
"higher math" is derived from primitives that have been proved correct.

[Anonymous No.5900145]

>>5900124
I don't care about limits.
1.The series clearly has a sum that can be derived from N(number of members).
2. these sums do no change or grow
3. at any point the sums just switch between two values. Its obviously not divergent or random. Its STATIC. Where do these series can diverges to?
Perhaps we should call it dual-convergent series since it converges to two numbers.

[Anonymous No.5900150]

>9:: (1/(10*10*10...))*(10*10*10...)=0*(10*10*10...)
>but we can cancel out the combined divisors from both sides! x/y=z x=z*y
You just divided by zero.

[Anonymous No.5900159]

>>5900145
>I don't car about limits
Then you'll not get anywhere with infinite series

On the rest, you are inventing non-standard meanings for mathematical language. Fine, so long as you are consistent, but you will have trouble reading and contributing to the body of mathematical knowledge, and you will miss out on a well developed set of definitional standards for no gain.

[Anonymous No.5900163]

>>5900145
You know a limit is basically the value the sum takes? What does it mean if you don't care about them?

[Anonymous No.5900197]

>>5900138
> Also you are opperating on non-similar series, one side is a limit*. The other isn't.
I operate on TWO SAME EXACT ABSOLUTELY EQUAL SERIES ON BOTH SIDES OF THE EQUATION. Don't try to muddy the water.
I never used a limit, i operate on series, their sums and products. If you assume i have used(not discussed, since all of you have the strange obsession with limits) a limit anytime, you must be mistaken. If you still see limits anywhere, that was not my intention. I have intended to use plain math.
>Exactly that is the point. you are using properties that only limits have, while not using limits hence the 'applying properties to series that only limits have'.
I don't intend to complicate this but series has the properties
1.first member value
2.operations between members
3.common ratio
4.number of members
5.final value/sum/product which can be expressed as variable.
If you think that #5 is a limit, its not: its the complete result.
> You say 1/infinity=0 it is not true, only 1/n as n-> infinity=0. That is a limit.
I say that logically
for ANY positive n
1/n will be a positive result greater than zero
and for ANY negative n
1/n will be a negative result less than zero
It doesn't take any "limits" to understand:
division of 1 by a number cannot produce zero
since if 1/x=0 there would be x that gives x*0=1 which is absurd. furthermore the sign of divisor applies to result, because division of positive number by negative number makes the result positive, and division of positive number by positive makes the results positive.

> You are missing the understanding of limits.
I don't see the point of USING limits at all, i use a intuitional/inductive model of series.

[Anonymous No.5900200]

>>5900163
>You know a limit is basically the value the sum takes
More accurately, the "sum" is a limit.

[Anonymous No.5900204]

>>5896730

>implying 0.9999.. is even a number

numbers must be finite, that's why you have extended real line, 0.999... is a process with limit in 1.

[Anonymous No.5900206]

>>5900204
numbers must be finite


Oh, hi, Pythagoras

[Anonymous No.5900207]

>>5900140
That not an oxymoron.
the laws of logic are supreme.
common sense/intuition just have a priority.
formalism/axioms/forced abstractions don't get priority.
You can't grasp this hierarchy, are you confused?

[Anonymous No.5900211]

>>5900142
>"higher math" is derived from primitives that have been proved correct.
real analysis derived from properties of the real number system which rely on archimedean property which relies on infinitesimals being absent i.e. it RELIES on 1=0.999...
My proof just make real analysis and any derivations from real analysis or real numbers look like a complete joke. Welcome to "higher math"

[Anonymous No.5900213]

>>5900150
>You just divided by zero.
There are no zeroes. the product of series(10*10*10*..) is larger than zero at any step.
Please reread the line you quoted.

[Anonymous No.5900214]

>>5900206

even Pi or square root of 2 are not true numbers, they exist only as limits. Only true numbers are natural numbers. get on my level, plebs

[Anonymous No.5900216]

>>5900159
If the mathemathical community will want to learn something from me(which is unlikely) it will be forced to use my definitions.

[Anonymous No.5900221]

1¸/3 = 0.33333333333...
3* 1/3 = 0.99999999999...=1

QED

[Anonymous No.5900222]

>>5900163
I use the abstraction of series sum/product as a concrete variable(dependent on series properties as described in >>5900197 ). You insist that i use a vague bound(which you call a limit) to which sum/product "tends to" which is clearly inferior to the simple abstractions i use.
here is the definition of limit of series:
In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to".
>tends to
As the positive integer n becomes larger and larger, the value n sin(1/n) becomes arbitrarily close to 1.
> arbitrarily close
Notice the difference between limits and absolute results(sum/product) of series? can you grasp it yet?

[Anonymous No.5900224]

>>5900221
Circular reasoning is not a proof.

[Anonymous No.5900225]

>>5900221
>QED
1/3 cannot be represented as decimal since the division never completes, 0.333...<1/3
using 0.333...=1/3 to prove 0.999...=1 is a form of circular logic. These recurring decimals are both approximate solutions, never absolute results.

[Anonymous No.5900229]

>>5900225

the word represents doesn't mean what you think it does

or are you trying to say I can't do floating point math?

[Anonymous No.5900233]

>>5900229
You can do floating point math, but you will not have a decimal representation thats exactly equal to 1/3. A flawed system can work.
analogy: Newton mechanics isn't accurate, yet it has some utility(just like FP math).
If you want to use 1/3 use rationals. You will not get any errors from use of FP numbers.

[Anonymous No.5900239]

>>5900229
1/3 can be never fully represented as a decimal.
The intermediate result of division of 1/3 can represented as 0.333... but it will just approximate result closer to 1/3 not 1/3.
Its basically this:
1.if we assume 1/3=0.333...
1/3= 3/10+3/100+3/1000+...
multiply by 3
1=9/10+9/100+9/1000+...
does this seem familiar?
1=0.999... now follow the counterproof at >>5896730 and you will see the premise is absurd

[Anonymous No.5900246]

http://en.wikipedia.org/wiki/Floating_point
However 1/3 cannot be represented exactly by either binary (0.010101...) nor decimal (0.333....), but in base 3 it is trivial (0.1 or 1×3−1)

The obvious alternative is to switch to base 3.'But wait, what about 1/7? should we switch bases each time a fraction demands an exact representation? I think there might be some point about rationals...

[Anonymous No.5900308]

Everyone should read this
http://en.wikipedia.org/wiki/Infinitesimal_calculus

[Anonymous No.5900561]

>>5899969
>No one else can.
I wasn't talking about you specifically, you insipid egomaniac. I was talking about calculating entities. You (meaning anyone, even a computer) cannot ever write out all the numbers, but you (general case again) can know exactly what they all will be, thanks to knowing that it's the same thing out into infinity. Thus, the division is complete because we know the entire result; 9s forever. The series converges to a value, and thus it is exactly equal to that value at infinity. Be careful not to mix them up with sequences, which never actually reach their infinite limit.
You cannot do this with nonerpeating decimals like pi, because you don't get a repeating pattern that tells you what all values will be down the line; you have to calculate them. If you can't use the bar notation, the best you can get is an approximation that is only as accurate as you (general) are willing to compute.
Once again, math degree. I've sat through a couple lectures explaining exactly why your assertions are wrong. Most people make them until they learn how math works, but these are common and patently wrong beliefs. Amend yourself.

[Anonymous No.5900575]

>>5900239
You have been proven wrong time and time again and refuse to accept it, it is a waste of time arguing with you. If you actually want to learn, understand the solution to zeno's paradox.

[Anonymous No.5900644]

>>5900561
> can know exactly what they all will be,
I don't dispute this, i dispute their equality to 1/9
>Thus, the division is complete because we know the entire result; 9s forever(you means 1's.its 1/9)
The entire "result" approximate 1/9 but never reaches it: if it was complete there will be no remainder. Division never stops: its absurd to claim that at ANY POINT(even infinity) the division stops, since theres a remainder at ANY POINT.
Inductively if there is remainder at 0.1,0.11 and 0.111 there will be a remainder at any digit.
Is that hard to comprehend?
>Be careful not to mix them up with sequences, which never actually reach their infinite limit.
Wrong 0.111... can be represented as a sequence
0.111... is a sequence 1/10+1/100+1/1000...

assume 1/9=1/10+1/100+1/1000...
multiply both sides by 9
1=9/10+9/100+9/1000...
1=0.999... which is disproved again here >>5896730
> math degree
Argument from authority
>Amend yourself.
You didn't prove anything i didn't refute. There is no point to "amend" anything, you have to reevaluate your dogmatic position about people with "patently wrong beliefs".
>>5900575
>You have been proven wrong time and time again and refuse to accept it
Nope. view the thread. All your arguments have been refuted. None of my arguments have been disproved. Its is you who is in the wrong: your only advantage is popularity of your position.
>understand the solution to zeno's paradox.
Achilles and the tortoise: Achilles never reaches the tortoise because the time/distance described decreases in magnitude proportional to the "current distance to tortoise"(which decreases artificially along with time periods) which is by definition is further than tortoise current location(x).
The race described is incomplete: it views only the time before he reaches the tortoise(viewing shorter and shorter segments of race), not the entire race where Achilles easily overtakes the tortoise.

[Anonymous No.5900708]

>>5900644
>Argument from authority

No, it just means he knows more math than you.

[Anonymous No.5900719]

>>5900708
>he knows more religion than you
must be right

[Anonymous No.5900744]

>>5900719
OP, you're doing this for steps 8-13:
1/∞ = 0, and so (1/∞)*∞ = 0*∞
therefore 1 = 0

The term 0*∞ is an indeterminate form and has no definition without limits, because, using limits, you can make an expression of the form 0*∞ equal to any real number or to ±∞.

Otherwise you're assuming 0*∞ = 0, which is unconventional and leads to problems like the one you've found here. You break the number system by assuming ∞*0=0, so what do you want more a functioning number system or ∞*0 = 0? If you pick ∞*0 = 0 you're a demonstrably poor mathematician.

https://en.wikipedia.org/wiki/Indeterminate_form

[Anonymous No.5900787]

> using limits, you can make an expression of the form 0*∞ equal to any real number
if 0 *inf =X than x*inf=0 , if x*y=0 either x or y or both are zero. Inf isn't zero. so x is zero.
Any other result will be absurd. I don't know how you can generate "any real number" unless your limit abstraction is severely defective. For entertainment, i'll ask to produce 0*inf =10 using your "limit".
> which is unconventional
Time to break convention than
>You break the number system
That was my intention. A system(such as real numbers) which can be broken has no place in math.
>you're a demonstrably poor mathematician.
Notice, i don't operate on absolute infinity, i operate on sum/product of series which is countable and can be used as variable.
Nevertheless i consider all infinities a form of number which has either to obey the laws of math or be discarded.