>Scientists literally believe that .999999 repeating is the

well it literally is

>>35313221
No, it's always going to be less than 1. It will be infinitely small, but it's still not 1. 1=1 nothing else = 1.

There's no space for a number between .999... and 1.
Thus they are equal to each other.

>>35313246
1/infinity=0
Therefore the difference betweeen 1 and .9 repeating to infinity is 0 decimal places. As the 9's approach infinity the difference between 1 and .9 repeating becomes 0. Any 1st grader can understand this.

>>35313309
what about the number that separates .999... from 1? That's a number

>>35313347
Give me a number with a finite number of digits and you'll have proven your point.

x = 1/9 = 0.11111...
9x = 9/9 = 0.99999...
1 = 0.99999...

>>35313347
.999... represents infinite 9's.
You can not literally conceive anything between these numbers.

File: main-qimg-418ff2cf3623dd63566ee85df28e6a59[1].png (37KB, 572x182px) Image search: [Google]

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>>35313187

>>35313347
You're thinking of an infinitesimal number, infinitely small, which is not well defined in the real number system. It's not a coherent concept mathematically. There are systems that use infinitesimals however, like the hyperreals.

>>35313187

Scientists think 1+2+3+4+5+...= -1 or some stupid shit.

I'm assuming this a joke. You understand the concept that 1 divided by 3 is 1/3, yes? AKA .3 repeating. 1/3 x 3 = 1, yes? Thus, since 1/3 = .3 repeating, .3 repeating x 3 equals 1. So .9 repeating is the same as 1. Infinity is only a difficult concept if you're autistic.

>>35313537
https://en.wikipedia.org/wiki/Riemann_zeta_function

The problem is that the infinite sum definition only works when the real part of s is greater than 1. So by the analytic continuation, it can be assigned a value of -1/12, but it doesn't "equal" -1/12.

>>35313554
Because it works and is mathematically consistent.

I remember this being the most hotly debated thing at forums I used to go to.

>>35313187
>i can't understand, so it's retarded.

>>35313347
Really? What number is it, then?

>>35313852
>>35313371
You can assign that number whatever variable you may like. It's a logically valid concept.

>>35313334
>1/infinity=0

Then 0* infinity is 1

checkmate atheists

>>35313991
No, it isn't. 0.999... is infinitely close to 1, so there can't be a number between 0.999... and 1.

> scientists think you can sum an infinite series

nice try infinite means forever, it never ends
if you could sum it it wouldnt be infinite

>>35313187
1/3 = .3repeating
2/3=.6repeating
3/3 = .9 repeating and reduces to 1/1, which is 1.0

infinity and zero are both irrational and shouldn't be accepted in mathemathics.

>>35313187
You do not understand what infinite means? If there is infinite .9s how could it ever not be seen as one? What else could is possible be? It is infinite 9s.

>>35313187
Kek, I thought the same thing once

How about you take this meme thread to /sci/ where it belongs, OP

Only important issues are welcome on this board.

>>35313347
x = 1 - (0.999...)

>>35314016
If you were to plot it on a graph, there would always be a space between 1 and 0.999...
That space can be named.

>>35314111
Yes. That number would be x. That is a valid definition. Have you ever dealt with complex numbers?

I'm a math major and in one of my classes my teacher used the fact that .999...=1 and nobody even batted an eye. I think it's funny that only people that don't know what they're talking about argue over this.

>>35314265
you have all been indoctrinated.

>>35313187
1/3=0.333333333....
1/3*3=1
0.333333333....*3=1
contentcontent
You have been muted for 4 seconds, because your comment was not original.

>>35314265
Did he present you the mathematical proof for it? Else your classmates may just don't think for themselves since it is certainly unintuitive.

It is like the turtle and achilles. No matter how many 9's you keep adding you will never reach 1.

>>35314111
x = 0
i solved it

>>35314360
>unintuitive

irrational more like it. this guy explains why

>>35314031

>>35313309
There is no integer between 2 and 3, therefore 2 = 3. QED

>>35314121
I'm telling you, there wouldn't be a space.

>>35314421
An infinitely small space, yes. Else prove it.

>>35313334
1/infinity = +0 or -0. The zero here represents an infinitesimal value, it's not actually a zero.

>>35314265
You are Educated Stupid. Children will be blessed for Killing Of Educated Adults Who Ignore 4 Simultaneous Days Same Earth Rotation.

x = 0.99999999999......
10x = 9.9999999999........
10 x = 9 + x
9x = 9
x = 9/9 = 1.

>>35314444
>infinitely small space
So zero?

>>35313381
Now prove 0.22... = 1 in base three.

>arguing about "infinitely small spaces" when it's literally just about fractions

1-.999...approximately=0

>>35314264
n-no :(

pls no punish me robit

>>35314459
exactly
similarly: 0.9999...= lim1 != 1

>>35313554
1/3 is not equal to .33...
You can't represent 1/3 accurately in base ten decimal notation.

>>35314490
no, not zero. zero is nonexistence - nothing
the space would be infinitely small, the smalles possible number above zero.

>>35313347
If there was a number separating them, then it wouldn't be .999...
It would be 9x10-n. Something like that.

>>35314489
Nice try, but that's rounding, and your a faggot.

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>>35314489
wha...SORCERY!

>>35314678
due to the concept of infinity it is true, and not rounding.

>>35314678
How is it rounding? No rounding took plece there.

>>35314701
>>35314702
x = 0.9999
10x = 9.9990
9 + x = 9.9999
difference of 0.0009
Because in .99... it continues infinitely it's an infinitesimal value but there's still difference between 1 and .99....

>>35315061
In an infinite string there the same number of nines in the number even if you try to specify that theres an extra infinitesimal digit added.

infinity=infinity +1
infinity=infinity+infinity
we aren't talking about your example, those are two finite numbers.

>>35315158
>we aren't talking about your example, those are two finite numbers
Yes, i can't phisically type out an infinite number, so i used that as an example. But if that triggers your autism how about this?
We're arguing whether 0.999... = 1, but in the proof we're discussing anon put
>x = 0.99999999999......
>10x = 9.9999999999........
>10 x = 9 + x
I posit, that using 9*0.99...=9 as proof here is circular logic, therefore his proof is invalid.

>>35315311
I don't see how it's circular at all. he solved an equality.
he multiplied by ten then subtracted x and divided by 9 and x equaled 1. he didn't define 10 as equal to 9.999...

>>35315480
>he didn't define 10 as equal to 9.999...
He defined x as 0.99...
So in here specifically
>10x = 9.99...
>10 x = 9 + x
he is saying 9 * 0.99... = 9; that's circular logic when you're trying to prove 0.99... = 1.

>>35314469
>Yuor Educate Stupid.
>wonders why people are making fun of him

>>35315603
9 plus x is 9 plus .9999999...
which is 9.9999999...
9.99999.... minus x equals 9.

I don't know where you are getting 9*0.99... cause that's 8.99...1

>>35313554
1/3 isn't actually 0.333 repeating
it's just the closest approximation because we have a 10 digit number system
if we used a 12 digit number system, 1/3 would be 0.4 (1/3rd of 12), which would be distinctly different from 0.3999 repeating.
It's an issue of the resolution of our measurement tools

>>35315744
>I don't know where you are getting 9*0.99... cause that's 8.99...1
Yes, exactly. That's why i called him a faggot for rounding earlier. He is abusing the fact you can't type out infinite series, so when he goes form
>10x = 9.99...
to
>10x = 9 + x
it' doesn't look like he did anything wrong.
It actually should be
>10x = 9x + x
and since he defined x as 0.99...
it means hes claiming that 9 * 0.99.. = 9, while trying to prove 0.99.. = 1, thus - circular logic.

>>35315755
I'm surprised you understand enough about bases, but still don't quite grasp base n representations aren't unique so I can only assume you're merely pretending.

saying that 0.999 = 1 is like saying that pi = 4 because you can divide a pie into 4 pieces.

Anything can be anything if you correlate equations that have nothing to do with each other.

>>35315965
How in the fuck is it 9x + x?
9.999999.... = 9 + 0.9999999999..... = 9 + x

>>35313187
>>Scientists literally believe that .999999 repeating is the same as 1
>This is how retarded science is.

Prove that they're not equal.

>>35313187
But you accept that 0.999... exists?

>>35315965
It's an infinite string though. there are always more nines at the end of the string there is no end to it.

I don't know whether .999...=1 counts as an impossible equation or not, but I see nothing wrong with his proof that it's true

>>35316091
9x+x=10x which is true. it just so happens that 9x=9 when dealing with an infinite string.

>>35316105
0.infinity is less than 1
0.anything is less than 1
Learn how decimels work retard

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>>35313187
Sorry you're struggling with math anon

Keep trying you can do it

>>35316091
9 + 0.99... =/= 10 * 0.99..
unless
9 * 0.99.. = 9
He would first have to prove that
9 * 0.99 = 9
if he wants to separate
10x = 9.99...
into
10x = 9 + 0.99...

This thread confirms /r9k/ as brainlet board

>>35313187
Pi is exactly 3!!!

>>35316285
Prove that 9.999... - 9 != 0.999...

>>35316419
Prove that god doesn't exist. The burden on proof is on you, faggot, since you're the one claiming 0.99.. = 1.

>>35316456
>hurr prove that 2+2=4

>>35314459
If you're telling me that 'nothing' is smaller than something that's infinitely small, then you're not understanding the definition of smaller.

>>35313187
.999... + .999... = 1.989898...

theory invalid.

>>35314684
burn the witch!
oregano

>>35313455
>You're thinking of an infinitesimal number, infinitely small, which is not well defined in the real number system. It's not a coherent concept mathematically.

It actually is a fully coherent concept. In the 1960s, they finally got it settled that standard analysis and nonstandard analysis are both on equally valid theoretical footing, thanks to the groundbreaking work of Abraham Robinson.

However, many mathematicians prefer teaching calculus in a way that doesn't require taking the extra time to define infinitesimal numbers. That way, they can focus the course more just on tools for solving commonly-encountered problems.

There's a reason why your calculus textbook probably doesn't spend much time discussing infinitesimal numbers. It's because learning all about the hyperreal number system (which is the framework for defining the infinitesimal numbers) has too little "bang for the buck" as far as providing you with useful tools for solving common problems in comparison to all the extra amount of time it takes to cover the theory of infinitesimals. Nonstandard analysis is quite an impressive approach, but it requires teaching a lot of theory up front, which is often not the best approach in the introductory calculus classroom. Teaching too much theory up front can often cause students to "space out" and end up not really understanding the concepts in the end. (That was exactly what happened with the "New Math" that so spectacularly failed a few decades ago.)

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OwOwOwO

>>35316456
0.999... = x
9.999... = 9 + x
(9 + x) - x = 9

What now, retard?

https://en.wikipedia.org/wiki/0.999...
read this wikipedia page

>>35316194
>Learn how decimels work retard

Learn how circular reasoning works.

You simply assumed your conclusion. That's not considered to be a valid proof.

Son, it looks like you're in way over your head on this one...

File: fourDim2_1_1.jpg (30KB, 746x432px) Image search: [Google]

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Here is an illustration of why 0.999... =/ 1

>>35316932
This is an illustration of why 0.999...=1, unless you actually believe that Achilles can never catch up.

>>35316984
every time you add a .9 you also add a .1. therefore he never catches up.

>>35313187
Please tell me you idiots are trolling

>>35316757

Careful, boys, about using software to analyze this.

When most people talk about "0.9999... = 1" they're using the real number system.

But computers don't use the real number system. Instead, they use a subset of the rational number system. Using rational numbers to approximate real numbers can result in small errors.

What any computer software says about 0.9999... versus 1 is utterly irrelevant to whether they are equal or not in the real number system.

I can guarantee that Wolfram Alpha does not do its computation using the real number system. That's because the real number system cannot even theoretically be modeled using a finite amount of computer space and time. (In fact, computers can't even model the entire rational number system -- they can only model a finite subset of the rational numbers.)

>>35316932
That's a finite concept. 9.. is not finite. Irrelevant.

Gas the brainlets now.

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>>35317084
infinity + 9 = infinity + 8
infinity + 9 - infinity = infinity + 8 - infinity
9 = 8

>>35316932
ah yes, all motion is impossible.jpg

>>35316456
Here's a quick way to check since you're retarded:

find a number between 0.999... and 1.

>>35317135
ah yes good ol' not an arguement.jpg.

>>35317152
here it is:

0.01111...

>>35317152
1-.999... would be your number.

>>35317156
That picture doesn't show .999..., it shows the partial sum of an infinite summation that results in one.

Here's your test: find a number between .999... and 1.

>>35313187
.999999x10=9.99999999
9.999999999-.99999999=9
9/9=1
Kill you are self.

>>35317195
I must direct you here:
>>35317112

Does 1.999999~ = 2?

>>35317179
No

0.999... + 0.0111... = 1.0111...

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When did you realize that mathmaticians were literally retarded.

>>35317223
This doesn't actually show anything?

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>>35317250
Yes

x + 0.999... = x + 1

>OP ignoring all proof
Great thread
sage

>>35317250
Yes. This works for all of these types of fractions.

Consider this:

1/3 = .333...
3/3 = .333... + .333... + .333... = .999... = 1

>>35317266
no

0.999... + 0.0111... = 1

>>35317211
that was all kinds of retarded.

.25x10=2.5
2.5-.5=2
2/2=1
huurrrrrr!

>>35313187
The problem, OP, is that you think there is such a thing as '1' and don't understand that '1' is a conceptual and convenient way of representing 0.99999.... which is the reality of our universe and the infinite scales it operate within.

>>35317312
You're a fucking moron. I know what you're trying to say, but the real number to add would be:

0.000...1, or an infinite number of 0s followed by 1. But this isn't a number, it's equal to zero.

Sorry you guys this isn't a debate topic, if you deny it you're just wrong period.

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>>35317306
... huh. so it is.

welp

>>35317364
that is complete gibberish.

>>35317366
I am right.

>>35317397
It's gibberish to you because you don't understand math. Sorry anon.

Have you taken calculus 1? That's the issue here: none of you have

Learn about infinite limits

>>35317397

1/3 = .333....

3/3 = .333... + .333... + .333... = .999... = 1

disprove this

>you can't

>>35317414
math is tautology. in the same vein you could reflect any critique of for instance, Anselm's proof of God.

>>35317438
>1/3 = .333....

That is an approximation.

>>35317461
It's not an approximation anon. 0.3330 would be an approximation, one with error of 0.000333...

You don't understand number systems

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>>35317461
>doesn't know the difference between approximation and exact decimal representation

>>35317486
Anyone can understand your reasoning. It is not complex.

What is a bit more challenging, is understanding why your reasoning is flawed.

>>35317112
Infinity is not a number retard.

>>35317508
Big words from a small minded man

Explain why it's flawed. You keep saying "No, here's the answer"

Point out the flaws in this proof, or stop talking:

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

Point out a flaw. You can't. I'm done arguing, you're all retarded. Jesus Christ fuck r9k. You autistic faggots are just as retarded as normies.

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>>35317556
There is also no such thing as an infinitely repeating decimal.

>>35317572
>Explain why it's flawed.

I did. Let me just do it again:

>>35317651
Dude you're a fucking idiot. Look at this approximation of your claim.

https://www.wolframalpha.com/input/?i=0.99999999999999999999999999999+%2B+0.0111111111111111111111111111

0.999... + 0.0111... = 1.0111...

>>35317651
>There is also no such thing as an infinitely repeating decimal.

I know you're trolling but irrational numbers are real.

>>35317727
look here:
>>35317045

>>35317732
>irrational numbers are real.

That is gibberish.

>>35317757
>That is gibberish.
"I don't understand math"

>>35314265
Most math majors I've met are just mouthbreathing autists anyways who memorize and nothing else. It doesn't take intelligence to be a math major, it takes soullessness and an utter lack of ambition

>>35317757
please don't troll /r9k/, my autism can't determine what's being said seriously

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>>35317757
>I'm right and the entirety of modern mathematics is wrong
>I don't have to prove myself, modern mathematics does

>>35315666
>not recognizing the masterwork of Time Cube

Show me on a numberline where you can separate .999 repeated and 1.

You guys know there is no actual conclusion to this argument right

>>35313187

You can make the argument that .9999.. repeating is not equal to one.

The problem is you'll have to make this argument using some kind of concept of an infinitesimal by extending the definition of the reals

You'll find that this is just not useful because it's never a necessary thing to do when you are trying to actually get useful results

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>>35317801
>"I don't understand math"

Not an argument. Ad hominem.

>>35317846
>please don't troll

Not an argument. Ad hominem.

>>35317853
>I don't have to prove myself, modern mathematics does

Not an argument. Appeal to authority.

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>>35317956
Not an argument. Muh fallacies.

>tfw math is a human invention that only applies to our perception of the universe, but our theorems and laws end up being correct allowing us to find planets and black holes

Are we the master race of the universe? Aliens on suicide watch.

>>35317956
Pic is wrong, there are infinite 9s, another 9 can always be added. .111.. isn't a number, show me a fraction or sum of fractions that results in .111 repeated. .999 is created adding 1/3 + 1/3 + 1/3

3* (1/3) = 1

3* (0.333..) = 1

1 * (3/3) = 1

1 * (0.999...) = 1

low in content and somehow not origional

>>35318019
>.111.. isn't a number

neither is .999...

>>35318019
well this is dumb.

repeating 1s are created by 1/9. .011... would be created by 1/90.

>>35318045
Wrong, is this falsity what your argument is based on? If so, you have been defeated.

1/3 = .333 repeated
1/3 * 3 = .999 repeated = 3/3 = 1

>>35317956
The problem is that mathematically I can prove that .999=1. You can't prove your claim.

1/3 = .333...

3/3 = .333... + .333... + .333... = .999... = 1

QED

>>35318019
1/3=0.333...
1/9=0.111...

Oh my fucking God this thread. I am legitimately considering leaving r9k now. I thought there was some intelligence here. I don't know why, but I did. But you're all a bunch of idiots

0.999... = 1

If you don't understand why you're a fucking moron

>>35318077
>1/3 = .333 repeated

No.

.333 + .333 + .333 = .999
1 = .999 + .0111

numbers are not real anyway, they are conceptual and help us understand the real world in terms of quantity, it's logical 0.999... = 1 but it doesn't mean anything to reality

>>35318135
Take out a pencil and paper and divide 1 by 3.

>>35318135
Oh my God you're so fucking stupid it's not even funny anymore

1 - 0.999... = lim(x->inf){1/10^x} = 0

>>35318135
.0111.... doesn't work as the completion of your summation though, because it leaves you with repeating ones, not zeros.

Let's do a partial summation to prove this:

.9999999 + .0111111 = 1.011111

>>35318177
I've literally pointed this out to him twice already. He's too stupid to understand or he's a troll. Either way, fuck him.

>>35318153
>>35318164
>>35318177

I refer you to my post here

>>35317651

1/9 on calculator = .111111111111111111111111111
2/9 on calculator = .22222222222222222222222
3/9 on calculator = .33333333333333333333333
.
.
.
8/9 on calculator = .88888888888888888888888
9/9 on calculator = 1

Fucking EXPLAIN this.

1 = 3/3
1/3 = .333...
3*1/3 = .999...
3*1/3 = 3/3 = 1
.999... = 1
explain why this is wrong

>>35318197
There is such a thing as a repeating decimal though.

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>>35318197
Okay kid, have fun

>>35318197
Also your summation is incorrect??

>>35313187
>Scientists literally believe that .999999 repeating is the same as 1
No, they just believe that .999... is infinitely close to 1.

Which for all intents and purposes makes it practically the same as 1.

>>35318234
Yes, but every time you repeat it you add a distance to 1.

$0.999... says this retard denying it is also a trumpster

>>35318261
this is gibberish.

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>>35318197
Why don't you go to /sci/ and make a thread showing your grand hypothesis?

>>35318285
.9 + .1 = 1
.09 + .01 = .1

and so on, and so forth. etc.

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>>35318301
The inner turmoil you feel is a result of impotence. I have no such problem since I am secure in my knowledge of always being correct.

>>35318329
right, but .99 + .011 doesn't make 1, which is the math that you're suggesting.

ALL OF THIS IS STUPID I HAVE THE ULTIMATE ANSWER TO THIS QUESTION FAGS.

.999... does not equal one but it is so close we can say "It's basically one." and call it a day.

>>35318274
haha le drumpfters amirtie?? u watch oliver too fellow genius?

>>35318379
No, it literally does equal 1. Sorry anon. This isn't a "middle ground" situation.

>>35318374
>right, but .99 + .011 doesn't make 1

Yes I know this.

>>35318356
Then your knowledge in adverse respect holds no significance to anyone else, since it is only your concern that it may be correct.

>>35318379
It does equal one though. It's literally the exact same number.

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>>35318045
>>.111.. isn't a number
>neither is .999...

I swear, I'ma gonna screen cap this thread if you guys keep on acting this retarded.

Pic related.

>>35318404
You say this, but my knowledge is what allowed me to put you into despair.

>>35318402
then you acknowledge that you're wrong, because adding more 9s and more 1s doesn't make it correct.

>>35318379
This is the correct answer. Mathcucks on suicide watch.

>>35318453
I am right that there is no such thing as an infinitely repeating decimal. The other part was le epic ruse.

>>35318430
You're taking a reaction image too literally. It is only a humorous exaggeration of emotion that may as well not exist in truth.
Your knowledge holds neither meaning nor foundation nor relevancy.

>>35318379
There is no such thing as "close" when you're talking about infinity.

>>35318488
>I am right that there is no such thing as an infinitely repeating decimal

But there is, for example, 1/3 = .333... and 1/9 = .111.

Technically .111... isn't even real it is just a product of our base 10 system. If we had a base 9 system 1/9 would equal .1 and 1/3 would equal .3.

>>35318551
It's real in the mathematical sense that it belongs to the set of real numbers.

>>35318528
>But there is, for example, 1/3 = .333... and 1/9 = .111.

You can conceive of cutting 1 apple into 3 parts. 1/3

You cannot conceive of an infinitely repeating decimal. 0.333...

>>35318583
Sure I can, I just did. .333....

>>35318580
Yeah but it really is just the fraction 1/9 in decimal form which we can't properly represent with base 10. There is no such thing as .111... or .333... or .999... it is all just glitch essentially.

>>35318619
Well what does it really mean? It means you keep adding decimals.

However, no matter how long you keep adding decimals you will never reach an infinite amount. It is in inconceivable.

>>35318629
These numbers exist and are real, they are exact decimal representations of fractions and are countably infinite.

>>35317280
The secret to science is being to lazy to chase accuracy. This is why we invented significant figures, to represent how lazy we are at any particular time.

>>35318644
"inconceivability" has nothing to do with the reality of a number. Graham's Number is inconceivably large but it still exists.

>>35318677
It's not laziness, it's recognizing the inherent inaccuracy of measurement instruments. A pair of calipers with a surface tolerance of a hundredth of a millimeter can't be more precise than that because its very manufacture precludes that.

>>35318682
>"inconceivability" has nothing to do with the reality of a number.

Then you have thrown reason out of the window.

If 0.999~ equals 1 then why does 0.99999999 - 1 equal 0.00000001 instead of 1?

>>35318650
But only in base 10. In base 9 (which would not have the number 9, 10 would actually be 9) 1/9 would be .1 which is a decimal which clearly stops.

>>35318511
I'm infinitely close to kicking your ass right now.

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.999 = 1?

That honestly makes me angry because it doesn't make sense

How can a recurring decimal be equal to 1?

At this point I might as well question the legitimacy of maths

Nobody has successfully even proven why 1 + 1 = 2

>>35318379
>.999... does not equal one but it is so close we can say "It's basically one." and call it a day.

If you insist on going down this road, here's the right approach:

The real number system is not capable of telling the difference between 0.999.. and 1. You may choose to perceive a difference between those two numbers if you like. But regardless of your choice, the real number system does not have the ability to tell the difference. Informally, you can think of this lack of ability as a kind of "fuzziness of resolution" that the real number system has. Thus, if someone insists on operating within the confines of the real number system, then that "fuzziness of resolution" will prevent them from being able to perceive any difference between 0.999... and 1, and they will be forced to conclude that the two numbers are equal.

Another thing to realize is that a number system does not necessarily have to have a perfect 1-to-1 correspondence between numbers and the digits that represent them. For example, in the rational number system, 3/4 and 6/8 represent exactly the same rational number, despite the fact that they use different digits to do so. (In fact, for every rational number, there is an infinite number of different digit sequences you can use to represent it.) We have the same kind of issue in the real number system too: 0.999... and 1 represent exactly the same real number, despite the fact that they use different digits to do so.

Perhaps it would be nice if a number system had a perfect 1-to-1 correspondence between numbers and the digits that represent them. If that's an important property to you, then I might recommend using the integer number system. But if you need more power than the integer number system can provide, then you'll have to pay a price for that additional power. And one price you have to pay is that you can no longer have a perfect 1-to-1 correspondence between numbers and the digits that represent them.

>>35318893
>Nobody has successfully even proven why 1 + 1 = 2

It is not proven, it is simply defined that way.

.999 is not one, but in many situations it can be rounded to one to simplify calculations without causing any harm to the quality of the output.

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>>35318893
Yes. It has been proven that 1+1=2.

Recurring decimals are a notation representing numbers. Numbers are abstract concepts

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 aren't the only digits. We could define a new number system where 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F are digits (in fact this is widely used and it's called hexadecimal, and this 0.999... problem wouldn't exist. In that number system, 0.FFF... = 1, A.FFF... = B, etc.

>>35318893
It's called axioms. We accept that 1 + 1 = 2 because it is so clear and apparent. Of course you can be a memelord and say you don't even know what a 1 or a 2 is or + for that matter but that is basically rejecting the definitions.

0.999... isn't a number for the same reason infinity isn't a number.

>>35318971
Oops 10 is not a digit obviously. Mistyped.

>>35319043
No you didn't you just don't understand what you are talking about. I'm onto you.

>>35318056
1/99 you mean, periodic fractions are always 9 or 99 or 999 etc in the denominator

>>35313187
I think this is the oldest kind of bait thread. OP, are you a meme archaeologist?

>>35318941
Damn, this was actually a really good explanation.

>>35314511
x = 1 / 2 = 0.111....
2x = 2/2 = 0.222....
1 = 0.222...

>>35318976
>We accept that 1 + 1 = 2 because it is so clear and apparent.

Well, YOU might accept it because it's "apparent", but I can assure you that serious mathematicians don't accept things just because it "feels apparent" to them. Instead, they create logical frameworks to develop the concepts from the simplest principles imaginable. And 1+1=2 is not the simplest principle imaginable -- not by a long shot.

For an example of how a logical framework can be used to define numbers, see the following:

http://www.math.uchicago.edu/~may/VIGRE/VIGRE2011/REUPapers/Lian.pdf

> Abstract.
> This paper sets out to explore the basics of Zermelo-Fraenkel (ZF) set theory without
> choice. We will take the axioms (excluding the axiom of choice) as givens to construct and define
> fundamental concepts in mathematics such as functions, real numbers, and the addition operation.
> We will then explore countable and uncountable sets and end with the cardinality of the continuum.

>>35317956
you'd need to add a one at an infinite-th decimal point for it to work though.

>>35318629
An infinite decimal expansion is defined as a limit, in this sense 0.333... and 0.999... are exact points.

>>35319234
>An infinite decimal expansion is defined as a limit

infinite: without limits

>>35313347

You're talking about uncountable numbers, you can go on forever with those and it would still make sense. There is no point having an argument about this.

>>35319216
Are you trying to tell me that literally all of maths is just sets?

>>35319340
That is in fact correct, dear gentleman

>>35319381
Kind of makes sense actually.

>math
>science
shiggy

All this seems to prove to me is that math is fundamentally flawed, a perfect human creation.

>>35319340
Yes

There are objects. There is a set of operators. There are subsets of all possible operators that can be applied to sets of numbers where all combinations result in numbers still within that set. Etc.

>>35319453
It is not all of math. The mathmagician uses the concepts 'infinity' and 'zero' to pull rabbits from his hat.

Anything in math that is irrational relates to either of these concepts.

>>35319262
Don't be a semantic faggot, the expansion is 'infinite' in the sense that it is not represented by a finite string. The 'limit' exists in the sense that going arbitrarily far along the sequence keeps you arbitrarily close to a particular point. 0.333... in particular is defined as the limit of the sequence 0.3, 0.33, 0.333, 0.3333, .... which is 1/3 exactly.

>>35319453
ITT: People who don't math

>>35319453
Mathematics is always going to be limited but this is not why. The '0.999... = 1' thing is not some fundamental untruth that is only true in math, all it's actually saying is that these are two notations for the same number not that two distinct numbers are equal.

It is possible to do analysis where there exists infinitely small numbers and yet 0.999... is still 1 simply because it's just a consequence of decimal notation not the axioms of math.

>>35319603
>the expansion is 'infinite' in the sense that it is not represented by a finite string.
> 0.333... in particular is defined as the limit of the sequence 0.3, 0.33, 0.333, 0.3333, .... which is 1/3 exactly.

You have not proven your nonsense. You have just comitted a tautology.

>>35319692
Why don't mathematics just agree to have one notation for one number? This is why Mrs. Turner gave me a D in Algebra...

>>35313187
Are you stupid
The whole concept of an asymptote acknowledges the exact opposite

>>35319692
>>35319676
You're assuming that I'm going from one unsolvable problem and not the many that fucking exist.

Unless you can go ahead and PROVE to me that math is a universal truth. Oh what, you can't? You just have to have faith that it is?

huh.

>>35318260
>No, they just believe that .999... is infinitely close to 1.

The correct way to say it is:

"IF you are operating entirely within the real number system, THEN 0.999... is equal to 1."

They don't use the term "infinitely close" in this case, because the concepts of "infinity" and "infinitesimal" and "infinitely close" (etc.) are not defined within the real number system -- so you can't use them, because the IF clause above said that you must operate within the real number system. Instead, they take the concept of "equal" and they expand it to include convergent power series. (FYI: 0.999... is the result of a convergent power series.) And I can assure you, mathematicians argued for a long time (mostly in the 1700s) about the appropriateness of expanding the idea of "equality" to include the result of convergent power series. So I can fully understand why people on this thread are reluctant to do so. All I can say to you skeptics is: "Bravo -- be a skeptic -- but also realize that your skepticism has been very, very, very thoroughly hashed out by some of the best mathematical minds of the past several centuries -- so you might want to start by standing on their shoulders."

You are certainly free to develop your own number system in which 0.999... is not equal to 1. If you're interested in doing so, then I might suggest learning about the hyperreal number system to give you some ideas. I would certainly encourage all interested students to play around with possible designs for other number systems -- however, it's quite important to understand exactly where the boundary of the real number system is located, and when you've stepped outside of it.

it's like an asymptote it's not actually one but it's close enough for it not to make a difference

>>35319762
this on a hundred thousand levels
/thread

>>35319820
You keep talking about "real' numbers. Are you tellin me there are "fake" numbers?

>>35319887
you fucking moron get out of this thread you clearly have no taken a math course.

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>>35319887
>>35319931
I can't believe someone fell for this shit

>>35319698
You can prove that 1/3 and the limit of the sequence 0.3, 0.33, 0.333, ... are equal by geometric series. Unless you mean something else needs to be proven in which case no it doesn't, it's a fucking definition you mongo.

>>35319855
No, 0.999... in this analogy is the asymptote itself which is 1.

>>35319340
>Are you trying to tell me that literally all of maths is just sets?

There are mathematicians who are interested in seeing if it's possible to define all of mathematics base entirely on sets.

Basically, it's an exercise in elegance. They believe that if you could define all of mathematics based on the smallest possible postulates, then they will be using the most "elegant" approach.

Now let me directly answer your question about what mathematics is:

Mathematics is a catalog of objects and their properties. In constructing that catalog, we tend to focus on objects that are defined as the result of patterns -- and especially patterns that can be built up in a straightforward way by repeating simple sub-patterns. So, for example, we find the set of natural number listed as one of the objects in the catalog of mathematics, because it can be defined using simple repeating patterns. But we do not find "banana" listed in the catalog of mathematics, because its patterns are considered to be too complex. But we do find certain kinds of snowflakes listed in the catalog, because their patterns are simple and regular enough to warrant inclusion (see the Koch snowflake). Along with each object, the catalog also lists all of its known properties.

It's important to understand that Mathematics is just a catalog -- and nothing more. That's what helps you understand, for example, that "real" numbers and "imaginary" numbers both exist -- and neither of them "exists" any more or less than the other. They are simply two entries in the catalog -- and there is absolutely no question that both of those entries "exist" in the catalog.

>>35320058
i get that, but it's still close enough to the point that any minute amount could be added to this number and it would be over 1

EX: 0.99999999999 + 0.0000001 = 1.00000019999

so it's an asymptote close enough to 1 to the point that any amount no matter how small would make that 1

>>35320009
Exactly. .999... doesn't mean infinitely repeating decimals, it is just a symbol you have defined to mean 1.

>>35313187
This plays into the goys pricing schema you see. This is how the Jew works, he twists and turns anything to his advantage until it is seen as 'normalized' example: 29.99 vs 30.00. the Jew knows this .01 difference plays a vast psychological role on your average normie when it comes to making purchases. He ensures Lobbyists will keep it this way in order to further his agenda.

>>35318379
>.999... does not equal one but it is so close we can say "It's basically one." and call it a day.


No, retard. Perhaps I should remind you that .9 repeating is a number.

That means it has it's place on the number line somewhere. Which means that it's not "getting" anywhere. It doesn't move. It either equals 1 or it doesn't (it does of course), but it doesn't "get" closer to 1.

For the dumbasses that still think it doesn't equal 1: Tell me, how much less than one is it? No really. What is 1 minus .99999999.....?

1-.9=.1
1-.99=.01
1-.999=.001
1-.99999999=.00000000(1?)

Really? You're telling me somewhere after the infinite zeroes, there's a 1? No, retard. Obviously not.

Or how about this: what is the number directly between .9999999999 and 1? If they're different numbers on the number line, obviously there has to be something directly between it?

Retards, all of you. Fuck you.

>>35319887
>You keep talking about "real' numbers. Are you tellin me there are "fake" numbers?

That's an excellent question.

The term "real" that is used in "real number" is not related at all to the ordinary English definition of the word "real".

Instead, the "real" in "real number" is merely technical mathematical jargon.

Mathematicians use a number of technical jargon words that are borrowed from English:

"natural number"
"rational number"
"irrational number"
"real number"
"transcendental number"
"imaginary number"
"complex number"

In every case, the adjective is merely technical jargon, and its meaning has no correlation whatsoever to its meaning in ordinary English.

I address this issue a little bit at the end of one of my earlier posts:
>>35320149

>>35320308
That was very rude of you anon. I am just here to learn like all of you and you didn't have to lash out on me.

>>35320308

Here's the thing. You said ".999... is equivalent to 1."
Is it the same value? Yes. No one's arguing that.
As someone who is an expert mathotologist who studies numbers, I am telling you, specifically, in mathematics, no one says .999... is equivalent to 1. If you want to be "specific" like you said, then you shouldn't either. They're not the same thing.
If you're saying "1" you're referring to the multiplicative identity value of the field that defines real numbers, which includes things from rational numbers to irrational numbers to pi.
So your reasoning for equalizing .999... to 1 is because random people "say they're the same value"? Let's get 1.000.... and -ei*pi in there, then, too.
Also, calling two numbers equivalent or not? It's not one or the other, that's not how mathematics works. They're both. .999 is equivalent to .999 which has the same value as 1. But that's not what you said. You said .999 is equivalent to 1, which is not true unless you're okay with calling all infinite sequences for which the limit is 1 as 1, which means you'd say 1.000... is equal to 1, too. Which you said you don't.
It's okay to just admit you're wrong, you know?

>>35320308
>You're telling me somewhere after the infinite zeroes, there's a 1

Yes, but there isn't an end to infinity, for the same reason .9999999 isn't equal to 1

>>35320420
>Yes

Okay, so you're retarded.

>but there isn't an end to infinity

So here you just immediately contradicted yourself. You said there's a 1 at the end of infinity, but then you said infinity never ends. Therefore there can be no 1 at the 'end' of something that never fucking ends.

> for the same reason .9999999 isn't equal to 1

No, dumbass. They're two different ways of writing the same number.

But go ahead. Challenge the rest of my post. If .9999999 exists on a number line somewhere less than 1, there has to be an average. So what is it? What is directly between .9999999 and 1?

There isn't one. Because they are the same number written in different representations: like 1.2 and 50% and .50. They mean the same thing.


Kill yourself.

>>35320491

>1.2

I meant 1/2

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You should be able to solve this.
This comment is oregano

>>35320491
>What is directly between .9999999 and 1?
.0000009

>>35320573
I meant .000000001

Wow our archaic number system has flaws wow
mind blown

>>35320385
0.999.. is equal and equivalent to 1

>>35320573
>>35320594

.9 repeating, I was just using shorthand.

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.999999999999999 = 1
=> 1-0.999999999999 = 1-1
=> .00000000...1 = 0
=> (1/0.00000000...1)(.000000000...1 = 0)
=> 1 = 0
hmmmmmmmmmmmmmmmmmmmmmmmmmmmm....................

>>35320615

it's a plebbit copypasta.

>>35320491
So you are saying .000...1 is not a number?

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>>35318971
>Mathematicians are so stupid, they have to prove 1+1=2 rather than just adding.

Honestly, after hearing both sides I think you both bring up valid points. I don't know which side to believe. I will just say you are both probably right in some ways.

>>35320599
but it's not a flaw it's a feature

>>35320716

of course not. if it's infinitely repeating than it never ends in any number other than 0.

>>35320564
The proof is trivial using Fermat's Little Theorem.

>>35320716
Yes, a number equal to 0

1 - 0.999... = lim(x->inf){1/10^x} = 0
.:. 1 = 0.999...

>>35320564
(1+n)^p isn't divisible by p because of an extension of the binomial theorem

n^p is congruent to 1 mod p is wilson's theorem so p divides n^p - 1

>>35320933
oh wait not wilson, fermat

>>35320918
>therefore dots
holy shit i can't stop laughing

>>35320385
Interesting post.

You are technically correct when you say that 0.999... is not "equivalent" to 1. That's because the sequence of coefficients of the power series that define them are not the same sequence.

However, I don't know if it's wise in this particular thread to focus the discussion on the difference between "A is equal to B" versus "A is equivalent to B".

The level of discussion on this thread is at quite a low level -- it feels to me like a discussion among, perhaps, students with average ability at the 10th grade or 11th grade level (referencing the USA educational system). I feel that at that level, it can do more harm than good to try to introduce more advanced concepts, when, in fact, it's apparent that many participants in the thread have not mastered the simple concepts yet. (My sincere apologies to those of you who have already mastered those concepts; I do not mean to insult your intelligence.)

My preference is to focus on the simplest possible statements that are technically correct, such as:

"In the real number system, 0.999... and 1 represent the same number, and therefore are considered to be equal."

I recommend we get that nailed down first. And in this particular thread, trying to get that one nailed down is kind of like trying to nail jello to the wall.

>>35320894
Do you even need that? Expanding (1+n)^p, and then subtracting n^p and 1, the first and last terms, the coefficient of each term is of the form p choose m, where m is between 1 and p-1, which is divisible by p.

>>35320999
>implying I want to go copy and paste the real alt code

>>35321007

I appreciate your response but it's literally just a Rebbit copypasta.

https://www.reddit.com/r/circlejerkcopypasta/comments/2ceq3u/heres_the_thing_you_said_a_jackdaw_is_a_crow/

>scientists believe the world is round
>scientists believe dinosaurs existed
>scientists believe evolution is real
You're not wrong OP, Sciencecucks are too scared of the real truths, they equate things as "HURR MUH SCIENSE OVERLORDS WHO ARE OBVIOUSLY PAID SHILLS BY THE ILLUMINATEY HAVEN'T PROVED IT SO IT CAN'T BE TRUE LALALALALA I CAN'T HERE YOU"

>>35321007
>students with average ability at the 10th grade or 11th grade level
Hey man I'm 29 years old.

>>35321035
You can do it that way, with FTL the terms are respectively congruent to 1+n,-n, and -1 (mod p), therefore the sum is congruent to 0 (mod p).

>>35313435
come up with that number
>you cant
are you really retarded or just simple

>>35321126

>scientists believe in climate change

literally lmaoing @ the """"scientific"""" method

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Well when I see something at the store that's 99 cents, I don't think "hey that's 99 cents" I think it's a dollar and I give the cashier a dollar and tell her to keep the change because pennies are useless.

>>35321247
The thing is, you fucking meme spreaders influence legitimately impressionable people. This is why fucking Trump got elected

You think you're being all funny spreading your retarded anti-climate-change memes and pro-Trump nonsense but you literally got a fucking moron elected who is literally a puppet to some alt right guy with zero political experience whatsoever.

You've fucked us with your memes, seriously

>>35321129
And again, I offer my sincerest apologies to those participants in this thread who were insulted by my comments.

I do believe I was reasonable when I estimated the mean level of understanding in this thread at about the 10th grade level. However, it's clear that this thread also has some quite talented participants. (A "high variance" as they would say in statistics.) And it's quite possible that you might be one of the more talented participants. Or, to be a little more blunt about it -- I would hope that at age 29 you would be one of the more talented participants.

>this entire thread going spastic when any math major will tell you it will always be less than 1
>just like the number of your girlfriends

>>35321256
This is honestly more valid reasoning than most people in this thread but you're still wrong.

>>35321299
Nah I suck at math.

>>35321313
>> any math major will tell you it will always be less than 1

Are there any math majors in the house who would care to corroborate this?

>>35321256
>pennies are useless
My penny jar disagrees with you.

>>35321483
I'm a math major, and it's 1, but I doubt anyone who thinks it's not will be convinced by this if they haven't been convinced by anything else in the thread.

Mathematics is a patriarchal construct.
Example, what if you have an even number that identifies as an odd number? The Patriarchal "logic" system you call maths can't deal with that.

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>>35321256
mfw this is one of the most reasonable posts in the thread

>>35321256
Anime Poster Fag proves entire thread wrong with ONE post!

>>35313810
Fuckin chuckled

>>35319453
I bet these brainlets don't even recognize the objective truth that the sum of all numbers ( 1+2+3+4...) is equal to - 1/12
Sad!

>>35321269

deal with it nerd, voting trump was the best decision i ever made

>>35321269
I know this is hard to swallow but Trump really was the good guy mate. Take a break from all the leftist media and just relax. He's not going to "destroy" anything.

>>35321656
By all numbers i mean all positive whole numbers, i mean.

>>35321656
That's a fun one, because the misconception about that is extremely common, even among professionals who should know better.

A good way to understand the misconception is to look at the geometric series (at n=infinity) versus its generating function 1/(1-x).

The two functions yield the same number, provided that |x| < 1.

However, just because two functions yield the same value within a narrow domain doesn't mean they're the same function. If they yield different results outside of that domain, that proves they're different functions.

If you make the mistake of assuming that 1/(1-x) is the same function as the geometric series, then for x = -1 you'll falsely conclude that 1-1+1-1+1-1... (without end) is equal to 1/2. However, the geometric series actually fails to converge at x=-1, which proves that the two functions are different.

So saying that (1+2+3+4...) is equal to -1/12 is the result of exactly the same kind of fallacy as saying that (1-1+1-1+1-1...) is equal to 1/2.

0.999... = (0.9 + 0.09 + 0.009...)

Sinf = a1
______
1 - q

a1 = 0.9 = 9/10
q = 0.1 = 1/10

Sinf = 0.9
_____
1 - 0.9

Sinf = 0.9
____
0.9

Sinf = 1

t. highschool pro

>>35322072
Youre wasting your finger strength, i must have a double digit iq, im just parroting literally unbeliveable pop math said by meme individuals

I remember how this topic created so much trouble in forums back in the day. No matter the fucking topic of said boards somebody would post this in their off topic section and you would get 300 pages of shit flinging.

>300 posts
fuck off faggots I ain't reading this shit.

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>>35317836
>hurr hurr durr I'm right because of my intuition and people who dedicate their lives to study the discipline are wrong.
Please kill yourself.

i haven't read any of the responses in this thread, but the fact that it has close to 300 responses is shameful. low quality bait for fat retards to bite

>>35317757
The real numbers are made up of the irrational numbers + the rational numbers.

Alright fags, now prove that P = NP.

>>35323595

n=1
why do people think this is such a hard problem lol

>>35323595
N=1. Easy peasy. Where's my fields medal and bags of money.

3*(1.33...) =3.999...

4-3.99...
=4 - [3+(9*10^-1)+(9*10^-2)...(9*10-inf)]
=1-[ (9*10^-1)+(9*10^-2)...(9*10-inf)]
=1*10^-inf
=0 ( anything to the power of negative infinity)

Difference of the two numbers is 0, so 3.99...=4

ITS FUCKING 1