/sci/ - Science & Math

>>11586483
That's what they actually believe, yes.
Less than 1 + less than 1 = 2.

>>11586483
>0.00...01 + 0.00...01 + .... + 0.00...01 = 0

>>11586483
0.9999999...+ 0.9999999...= 0.18181818181818...

>>11586483
>>11586495
So does .999... Signify the limit of 9/10+9/100+..., or is it just a sum of a finite number of terms? Because if it is a finite sum then yes it less than 1.

OP here, meant to make my text the funny frog colour to indicate I am NOT a 1tard and therefore I think the equation presented in the OP is WRONG
>>11586495
How can they really believe this?
>>11586500
This should be the predominant proof that 0.999 cannot equal 1

>>11586504
Don't try and complicate things 1tard I see you there. Clearly I meant 0.9 recurring

>>11586510
Okay so infinite sum so it is a limit and thus equal to 1.

>>11586516
So you are really saying the equation in the OP is correct... You 1tards are worse than flat earthers

>>11586504
Find the limit of .999 + .999

>>11586523
I don't think you understand the point of a limit. That's a finite sum...
>>11586520
>Ad hominem therefore I'm right and you're wrong.
yikes

>>11586523
He can't, because it doesn't exist- neither do infinitely recurring decimals.
>hurr durr what about pi hurrrrrrrr
The universe is not infinitely divisible, true circles do not exist. Pi is not real

>>11586504
0.999... is not a limit retard. The ellipsis means the pattern continues infinitely, not that you are finding a limit

>>11586530
Nope. If 0.9 recurring is real you should be able to add it to itself. Clearly it is not real otherwise.

>>11586530
No one here is talking about limits you mouth breathing fucking retard. We are talking about 0.9 recurring and I am asking you to add them together. If 0.9... is the same as 1, and 1+1 equals 2, then 0.9... added to itself is 2. How is it a finite sum if it is adding two infinitely recurring numbers? Or are you admitting they are not real?

>>11586537
Oh. .9 recurring. Sure, it would just expand to 2(9/10 + 9/100 + ...) = 2

>>11586542
You agree recurring implies infinite 9's, so it is only realized as a sum of it's decimals. You have read Apostol and understood decimal notation of real numbers, right? I mean, this is the MATH and science board, right?

>>11586544
Uh I don't need to read Aristotle to say this anon it's pretty simple that two numbers consisting of 9s can't add up to 2. If anything, >>11586500 is correct.

>>11586483
1+1=2

>>11586497
0+0+0=0

>>11586507
In the book and film 1984 the main character thinks 2+2=4 and the government wants him to not think that, they want him to think 2+2= whatever they say it equals. Near the end they torture him until he gives up and breaks down and says he doesn't know anymore what 2+2 equals.

The "0.999...=1" idea/concept, the reason it's taught in school and pushed as being true, it's probably because functions as a small tool (one of many) to break people's ability to think for themselves and to see reality clearly.

It completely contradicts what people already know and have already learned, but then as they get older they "learn" to accept as a truth that less than 1 is 1. That probably has some sort of subtle psychological effect on people that's beneficial to the ruling powers in society.

>>11586552
>0.9+0.9=0.18
your fields medal is in the mail

>>11586504
>if it is a finite sum then yes it less than 1.
It's infinite. Endless 9s. Which means it's forever less than 1.

>>11586565
>let's pretend finite is infinite

>>11586574
>lets pretend less than 1 is 1

>>11586565
I agree completely. If you can teach stupid shit that is obviously wrong like anything other than 1 being 1, and have that be the "truth", eventually you can make anything the trutch. 1tards are going to be the reason we are subjugated by a one world government. How very fitting

>>11586552
"Aristotle"

You absolute dumb fuck. I said Apostol, one of the most renowned authors of Real Analysis next to Rudin.

Can't wait for school to start again.

>>11586594
Anything? How about .5+.5? Oh wait, that is 1! So why can't a limit equal 1? We've shown things that when added become 1. >>11586573
>forever less than one
Riddle me this. .999... is a real number. So is 1. If .999... is strictly less than 1, use the density of the real numbers to find a number in between .999... and 1. This should be easy, since they're not equal, right?

you cannot define null point nine repeating without first defining infinity, and you don't have a working definition for infinity that means what your professors tell you it's supposed to mean, so null point nine repeating is only as good as a finite amount of nines. so of course it's less than one cause any finite arrangement of null point nines is less than one.

even cantor himself treated the word "infinity" more like the word "indeterminability", and his classes or sizes of infinity are actually just degrees of indeterminability. The order and structure of R is more complicated and indeterminable than the order and structure of N, for example. Large numbers as a product of the computer calculation age beginning in the nineteen-forties are also beyond the scope of cantor's mental midget mind, as large numbers themselves are too big to comprehend, which is practically the identical property attributed to modern "infinity" when used as a descriptor relative to numbers or amounts.

>>11586616
Real numbers can't have a density or they would have gravity and mass also. Can't you puremath tards think in terms of reality rather than your crazy schizo dreams for once?

>>11586626
Most based thing I've read all day. Thans anon. I don't think I need to btfo the 1tards anymore myself, I will simply save this text for next time

>>11586634
Okay hillbilly, the density of the reals property states that for any two numbers a,b such that a=/=b, there is a number c such that either a<c<b or b<c<a

>>11586575
lone shitposter vs world

>>11586616
Easy:
.999... < (.999... + 1) ÷ 2 < 1

Here is a proof to btfo 1tards with. Please copy and paste this to btfo 1tards in all threads

1-0.999...=0.00000000...000001

There are infinite 0s between the start of the number and the 1 at the end.
>hurr durr you cant do that
Well I guess you are saying infinity doesn't exist then? Because if there are infinite .9s before you get to 1 why cant you have infinite 0s before you get to .0000000000001?

1tards BTFO FOREVER!

>>11586646
What the fuck don't start bringing letters into this. I swear every time you mathtards get called out you just invent another layer of meaningless nonsense...

>>11586646
thats not real or even good thinking.

there is a number smaller than TREE-three by an arbitrary amount, but this number is indeterminable, just as indeterminable as TREE-three. There is a number larger than grahams number by an arbitrary amount and this too is indeterminable beyond possibly being smaller than TREE-three.

indeterminability is a real concept. a less than c less than b is only valid if a and b are determinable. null point nine repeating is indeterminable.

>>11586665
>There are infinite 0's
>there's a 1 at the end
Pick only one.

>>11586699
>there are infinite nines
>there's a one at the end
learn to read

>>11586699
Nope. Maybe your tiny 1tard mind can't keep up with concepts like this. If an infinite number can have a beginning, it can have an end. If infinite numbers can't have a beginning or end, 0.9... can't exist because we start at the beginning. If you flipped 0.0000....00001 around you would have 1. In reality, beginnings and endings are not different, nor do they truly exist. Only a brainlet would think that way

>>11586652
>schizo vs reality
Good luck.

This debate ultimately comes down to those who are too stupid to understand that physical stuff is not what math is about

>>11586665
>1-0.999...=0.00000000...000001
1-1=0
thrilling

>>11586483
>LOOK MUM. I DID IT AGAIN. HAHA
>that's nice sweaty.

>>11586665
You are an actual fucking moron if you seriously think this, please be trolling because it is truly a shame if there are "people" who think like this.

>>11586730
found the dropout

>>11586738
>gets totally rekt
>has no counter arguments
>resorts to insults

do we really need daily 0.999... =/= 1 threads? just askin

>>11586763
Op has to make his mum proud.

>>11586763
Absolutely. We need them until this misinformation is quelled. People that think 0.99..=1 really ought to be on some kind of banlist; their anti science (non empirically observable) viewpoints are damaging and dangerous.

>>11586751
You have an insanely low IQ.
>if you can have a beginning you can also have an end!
yes that's called being finite. An INFINITE thing does not have an end.

>>11586777
0.99 != 1
0.95 == 1

>>11586777
>science
math isn't science
protip: board's name isn't "/sci/ - Science & science"

>>11586681
>Arguing against properties of real numbers
Your fields number will arrive in the mail.

>>11586763
Apparently, since there are still some brainlets on /sci/ who genuinely believes it equals 1. There's not that many left, but they're a persistent and very vocal minority. We need to absolutely dominate them and humiliate them so they give up. By then, threads like these will be less necessary. By then, they'll just be useful as an occasional reminder to help younger anons not fall for the "=1" propaganda the few remaining determined trolls will no doubt still be pushing occasionally.

>>11586791
>number
medal*

>>11586780
>An INFINITE thing does not have an end.
You just admitted that it will never reach 1. Nice.

>>11586780
Loooooooool you got BTFO by >>11586797

>>11586797
>>11586816
How do you know something can't be represented in both an infinite and a finite way?

>>11586483
2 = (126/125)72(225/224)27(2400/2401)19(4375/4374)31

Get good bruh

>>11586840
2 = (1+1/(1·3))2(1+1/(5·7))2(1+1/(9·11))2(1+1/(13·15))2

peace

>>11586483
0.9999999... + 0.9999999 = 0.18181818181818...

>>11586495
.0000000~1 is immaterial
>t. Accountant

>>11586534
>0.999... is not a limit retard.
IT DEPENDS UPON CONTEXT
Does "lead" mean to take charge, or does it mean the chemical element? It depends upon the context it is being used. An ellipses may mean a limit, or it may mean a continued patter, maybe even a -completed- infinite pattern. But the ellipses cannot mean both things in the same instance, and some mathematicians make the mistake fo bouncing between both meanings in a single explanation, creating mistaken logic eleven kitty pepsi

>>11586848
Good bait mate

>>11586871
Me literally on the right. Same Chad jaw and everything

>>11586718
Based dicksucker

>>11586507
based retard

>>11586534
The ... means you're taking the limit of the sequence (0.9, 0.99, 0.999, 0.9999, ...), just like 1 + 1/2 + 1/4 + 1/8 + ... means you're taking the limit of the sequence of the partial sums.

>>11586483
>>11586495
>>11586497
>>11586500
>>11586504
>>11586507
>>11586510
>>11586516
>>11586520
>>11586523
>>11586530
>>11586531
>>11586534
>>11586537
>>11586542
>>11586543
>>11586544
>>11586552
>>11586553
>>11586556
>>11586565
>>11586568
>>11586573
>>11586574
>>11586575
>>11586594
>>11586597
>>11586616
>>11586626
>>11586634
>>11586642
>>11586646
>>11586652
>>11586661
>>11586665
>>11586674
>>11586681
>>11586699
>>11586699
>>11586718
>>11586730
>>11586733
>>11586734
>>11586737
>>11586738
>>11586740
>>11586751
>>11586763
>>11586775
>>11586777
>>11586780
>>11586788
>>11586790
>>11586791
>>11586794
>>11586795
>>11586797
>>11586816
>>11586822
>>11586840
>>11586847
>>11586848
>>11586849
>>11586861
>>11586864
>>11586871
>>11586900
>>11586936
>>11587098
>>11587106
x = 0.999...
10x = 9.999...
9 + 0.999... = 9.999...
9 + x = 10x
10x - x = 9
9x = 9
x = 1

>>11586871
>= less than 1
the guy who made this is a retard

>>11586483
3/3+3/3=6/3

>>11587112
retard 0.999... * 10 = 9.999...0
10x - x = 9.999...0 - 0.9999... = 9.000...81

>>11586483
do infinite decimals exist in practical reality though? serious question

>>11587293
Based

0.9999999...+ 0.9999999...= 1.999999...8

>>11587293
holy fucking based.....

>>11586733
You can't stretch that kind of thinking to saying math shouldn't have utility, though.
Physicality plays a larger role than you're probably willing to believe.

How many 9's are in 0.999...?

i don't know.

you don't know.

therefore, it is indeterminable.

>>11587293
That were true if you were talking about omega (the smallest ordinal infinity) 9's, but that's not what this is about. This is about a truly infinite, ever-continuing stream of 9's. There is per the idea of ... no last 9.

>>11587297
>>11587306
Always using le epic /pol/ vocabulary doesn't make you less retarded

>>11587361
>/pol/ vocabulary

OK, genius here, came to enlighten you all. First, I think we can all agree that [math] \frac{1}{3} = 0.3333... [/math]. If you don't, please tell us what else it should be. Then [math] \frac{3}{3} = 0.9999 = 1 [/math]. Again, if you disagree, tell us what is wrong and why. So then, [math] 0.9999... + 0.9999... = \frac{3}{3} + \frac{3}{3} = 1 + 1 = 2 [/math]. The only alternative approach is to refuse digital approach and use fractions exclusively, which rids the concept of any ambiguity, like infinite decimal expansion. It also rids of the "numbers as processes" misconception.

>>11586534
source: my ass

>>11586531

DUES VULT! By GOD, Brother! Well said! You have put those GOD CURSED SODOMITES in their place with those eloquent facts!

Listen up, SINNERS, your time is over! We have had suffered enough, we are reclaiming the realm of mathematics for the FINITE and the DISCRETE! Maybe even have time to sack Constantinople on the way. DEUS VULT!

>>11587388
. 333... x 4 = 1.33...2
. 999... x 2 = 1.99...8

>>11587400
1/3 * 4 = 4/3 = 1 + 1/3 = 1.3333333
3(1/3) * 2 = 6(1/3) = 6/3 = 2

>>11586565

But no longer, Brother! We are fighting back! WITH GOD ON OUR SIDE! Sending Infinity, infinitesimals and recurring decimals straight back to HELL!

And do you know why? But of course you do! BECAUSE GOD WILLS IT! DEUS VULT!

>>11587400
>1.33...2
at which position is the "2" ?
>1.99...8
at which position is the "8" ?

>DEUS VULT!

>>11586495
>>11586483
>>11586500
Absolute retard

>>11587379
Disprove anything I said. You 0.999...-≠-1-tards always claim that we don't grasp Infinities but it's kinda obvious that you don't know about ordinal, cardinals and "limit infinity" since you always confuse the three. It is obvious that here we must apply "limit infinity" (which is the only "never-ending" of those three) since we have the "...", yet you always use ordinal Infinities when trying to disprove us.

Also
>implying I'm not a /pol/ user myself

>>11587602
cantor was a hack. shut up retard. you never tried to imagine even for a single moment what he was thinking about while he did math, which is not even in the scope of the fact that his ideas were outdated and archaic by the 1940's.

>>11587649
how exactly is cantor's work on infinities related to 0.999... ?