/sci/ - Science & Math

>>14585845
1. Real numbers only have finite place values (...hundreds, tens, ones, tenths, hundreths...)

2. Two numbers are the same if there's no number between them

3. Take the difference of 1 and 0.99999..., what do you get? Note 0.0000...1 is not a number, because of rule 1.

4. Conclude they're the same number.

>>14585845
flabby fattie

>>14585845
1. If x - y = 0, then x = y
2. 0.000... = 0
3. 1 - 0.999... = 0.000...
4. therefore 1 = 0.999...

>>14585848
>1. Real numbers only have finite place values (...hundreds, tens, ones, tenths, hundreths...)
Are ordinal numbers real numbers? If not, then why not just define something analogous to ordinals that fits between any two expressions of real numbers? i.e.
>Note 0.0000...1 is not a number, because of rule 1
would be an invalid inference under such a construction, because rule 1 would only prove it to not be a real number.

>>14585937
Yes, wasn't perfectly exact with that last statement, it would imply it's not a real number, which is the system in which the equality 0.9999... = 1 holds.

There's nothing stopping you from putting all the numbers you want between 0.999... and 1 in a different number system, assuming you can be consistent about it.

>>14585868
Looks more like edema

>>14585879
What is the largest number that is less than 1?

The number used to define a dedekind cut can be placed in either set

>>14585848
1-0.999... is a number though

>>14586076
Yeah, zero.

>>14586080
uhh no? the difference between two different numbers is not zero.

>>14586082
Then what digits does the difference have?

>>14586083
there doesn't need to be a well defined value

>>14586090
So your definition of subtraction can lead to undefined values? Seems... like a crappy definition.

>>14586091
the expression doesn't have to be solvable in regards to containing defined digits or symbols in current math notation for it to be valid

>>14586100
It does for it to qualify as a real number. Every real number can be defined in terms of a (not necessarily unique) digit sequence.

>>14586104
ok what digits does pi have? write the whole sequence out big boy.

>>14586120
It starts like 3.141 and can be derived from any number of infinite sequences to arbitrary depth, unlike your "undefined" answer to 1 - 0.9999...

>>14586017
0.999...8

>>14586133
dark matter did it

>>14585848
>1. Real numbers only have finite place values
Arbitrary rule that has no basis
>2. Two numbers are the same if there's no number between them
But there's a number between 1 and 0.999..
>3. Take the difference of 1 and 0.99999..., what do you get? Note 0.0000...1 is not a number, because of rule 1.
Yes it is, you're just making shit up on the go
>4. Conclude they're the same number.
Except they're not

>>14586138
>my made up rules are less arbitrary than your made up rules, wahh

>>14586149
Yes?
Since it's not applicable to reality it is clearly wrong, you can divide things into three parts without any problem but you can't here because our mathematical system is archaic and very flawed, you'll actually notice a lot of shit doesn't add up if you go outside and look around a little, you can't just say two things are the same when there is a very defined difference between them.

>>14586164
>implying math needs to relate or apply to the universe to be valid
This is your brain on physics

>>14586168
>a language which is entirely based on describing the physical dimensions and properties of reality needs to relate or apply to reality
Yes, retard

>>14586175
>a language which is entirely based on describing the physical dimensions and properties of reality
That's not what math is you assburger, that's literally describing physics.
The vast majority of PhD math has no application or relation whatsoever to reality. Deal with it.

0.333... * 3 = 0.999...
1 / 3 = 0.333...
3 / 3 = 1 = 0.999...

>>14586180
ok, now prove that 1/3 = 0.333...

>>14586179
Math and physics are interchangeable dumb faggot, they're two sides of the same coin
>The vast majority of PhD math has no application or relation whatsoever to reality
That's literally what I said in my previous post, most mathematics is just retards like you jerking eachother off for nothing
But guess what, 0.999... isn't 1 no matter how much cum you guzzle

>>14586193
You put your left foot in
You take your left foot out
You put your left foot in
and you shake it all about

>>14586195
There's literally math that you're claiming isn't valid because you're bringing physics into the conversation. The math works, no matter how much you don't like it, and no matter that it doesn't line up perfectly with reality.
Math doesn't give a shit about reality, only logical self-consistency. There is plenty of math that is useless for describing objects in our universe. That math is still valid math, even if it you think it's stupid.

>>14586193
Base 12
1/3 = 0.4
Rational result.

>>14586202
>There is plenty of math that is useless for describing objects in our universe. That math is still valid math
No it's not

>>14586217
>physics and math are the same if you just pretend all the other non-physics math isn't real
You're a fucking genius, your fields medal is in the mail.

>>14586126
where is it defined that a real number has to be able to be placed on the number line on a specific spot?

>>14586224
>things that don't apply to reality aren't real
Yes, retard

>>14586230
Math isn't real. Hate to break it to you. Not sure who told you otherwise.
Math is not real.

>>14586230
>The physical world constitutes the whole of reality
Materialists shoo shoo

>>14586227
"where is it defined that numbers have a value"
holy fuck anon

>>14585845
>if
A.BBB... = C
>then
C - D = A.BBB...E?

>>14586227
Various ordering properties imply it.
The Archimedean property implies that, for any real number x, there is an integer n such that n <= x <= n+1.
You can iterate this implication to show that you can bound any real number to an arbitrary accuracy of digits.

>>14586239
>he thinks his shitty alice in retardland calculations are applicable in explaining metaphysics when it can't even divide something into three parts

>>14586249
ok and?
one can place 1-0.999... at 0.0001 then 0.00001 etc. depending on the needed accuracy
not my problem some boomers didn't consider '...' when writing their deprecated proofs nor that the standard math signature doesn't define a functional symbol for this use case.

>>14585845
1/inf=0

>>14586285
>one can place 1-0.999... at 0.0001 then 0.00001 etc. depending on the needed accuracy
Which implies that every finite place value will be zero in the full expansion, which makes the number zero.
There are extended number systems where what you're saying is possible, but it's not possible in the reals, that sequence converges to zero and only zero.

>>14586289
>Which implies that every finite place value will be zero in the full expansion, which makes the number zero.
I don't see why it would imply that.

>>14586293
You're saying something like this:
1 - 0.999... < 0.0001
1 - 0.999... < 0.00001
1 - 0.999... < 0.000001
1 - 0.999... < 0.0000001
etc.
If you pick any place value in the number 1 - 0.999... (e.g. the hundredths place), then one of the above statements forces the digit there to be 0, (e.g. 1 - 0.999... < 0.0001).
Since you can pick any place value and conclude it must be 0, it means all the place values are 0.

This entire conversation is fussing about the limitations of base 10.

In base 12, 1/3 equals 0.4
The entire conversation ceases to exist.

>>14586312
Ah, but instead we have 1 = 0.BBBBBBBBB... in base 12

None mentioned that 0.9999.... is a geometric series?

>>14586307
I don't think so.
For any decimal place n that you pick on the right hand side there will be a decimal place n+1 that is equal to 1 on the left hand side.

>>14586323
Yes, for a finite n, and as n gets higher the zeros push that 1 further down in place value and it disappears in the limit because everything is eventually replaced with zeros.
There's infinitely many of those inequalities so you need to let n go infinite.

>>14586315
What fraction is that

>>14586351
B = 11 in base 12 by convention, so
0.BBBBBBBB... = 11/12 + 11/12^2 + 11/12^3 + ...

>>14586212
Is 4×12-1 equal to Σ(3×10-1i, i, 1, ∞)?

>>14586418
Sorry, 4×12^(-1) and
Σ(3×10^(-1i), i, 1, ∞). 4chan ruined my superscripts.

>>14586333
>because everything is eventually replaced with zeros.
But it's not because there's a 1 at the end of it

>>14585879
>3. 1 - 0.999... = 0.000...
wrong
it's .0...1

from a practical standpoint an even weaker claim is true

that's all that matters

>mathrannies btfo

>>14586333
if we can have 1 at n=infinite on the right hand side then that is the number we are looking for to equal 1-0.999...

>>14585937
What you are referring to are called surreal numbers and are literal joke in math. No one uses them for any real or indeed "un-real" purpose, they are purely wank.
I hope this answers your question.

>>14587498
>they are purely wank
In this instance I'd call it more of a shitpost.

>>14586285
damn
>>14586289
won that debate

>>14587498
Also I am genuinely curious whether ordinals are real numbers.

>>14586133
I see, I guess I never realized that 8+1=10

>>14586017
There is none. If one chooses any number less than 1, we can always choose a number higher than that, but still less than 1.

Let's say X is the largest number less than 1. Then we see that 1 > (1 + X)/2 > X (that is, we have a new "largest number less than 1"), which is a contradiction of our assumption.

>>14587541
That is just a giant cop out, and is like saying 1=2 in integers because nothing exists between them.

Because 0.999… =/= 0.999…9

>>14586682
this is the most retarded take in the entire thread

>>14585845
This made me realize how retarded most mathematicians are. It's not even about whether it's true or not. It's that all the popular proofs are so obviously wrong but still taught in school and textbooks everywhere.

>>14588126
Wrong how?

0.9999... is NOT equal 1 but it is quite close. So, we can make an approximation. We can say, 0.9999... is approximately equal to 1. Like this,
0.9999...≈ 1

>>14588127
Depends on the proof. Pick one of the popular ones and I'll tell you.

>>14585845
Precision problem, what else is to explain. For an infinite periodic 0.9999..., it is unironically and practically 1

>>14588128
The problem comes from conversion across asymptots using a different convention.
9/9 = 0.999... = 1 = 1/1
Following this convention
1/10 = 0.1
9/10 = 0.9
99/100 = 0.99
999/1000 = 0.999
999.../1000... = 1?

>>14588689
>999.../1000...
inf/inf is undefined

Was it the food or the water?

>>14588132
>Pick one
https://en.wikipedia.org/wiki/Geometric_series#Proof_of_convergence

>>14588745
then 9/9 is undefined as well...

Is 0.111.../0.111... undefined as well, even though its 1/9/1/9?

>>14588745
>>14588777
Said another way:

x ^ (1/n) approaches 1, but is never 1.

>>14588782
This can be shown experimentally with:
(x ^ 2) ^ 0.5 does not equal (x ^ 0.5) ^ 2

>>14588689
>999.../1000... = 1?
999.../1000... = 0.999...

>>14588787
So 999.../10000 = 0.999...
But 999.../999... = 1?

>>14588796
This would mean that 9 * 0.111... = 1?

You see there is a fundamental flaw here.

>>14588777
>then 9/9 is undefined as well...
for you, sure

>>14588810
So then 9 * 1/9 = undefined?

>>14588819
for you, sure

>>14585845
They're equal because we define them as equal within our number system

>>14587519
Anybody? Bueller?

>>14588752
What you link is correct. But it doesn't prove [math]0.\bar{9}=1[/math].

>>14589659
aww it's retarded

>>14586727
>>14586651
As soon as you start trying to put digits at the "infinityth" place you're no longer operating under the rules of the real number system. Either you ditch that system or work inside of it, but you can't have a real number that has a one at n=infinity.

>>14589884
*cough*
1/9

>>14589901
Still doesn't have a 1 at the "infinityth" place. The concept of "infinityth" place value has no meaning in the real numbers. For example, what's the "infinityth" place value of Pi, or 1/7?

>>14589972
so it's a 3 then, got it

>>14589984
lol, whatever you say anon