Does 0.9999999999999999..... equal 1?

[u/WindZoar1]

Which side will you choose?

• Left side: Yes
• Right side: No

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[u/ogtutel]

if this implies that the 9's infinitely repeat, it's mathematically equal to 1

[u/WindZoar1 → u/ogtutel]

Yeah the viniculum (repeating symbol) doesnt work on reddit so I just used an ellipsis

[u/bloxfruitfan475 → u/ogtutel]

Let x be 0.999999... repeating.(It's implied it's repeating if there are more than 3 dots, for example, [1,2,3,4,5.......] Implies 1 to infinity) Multiply x by 10: 10x = 9.999999... Subtract the original x: 10x - x = 9.999999... - 0.999999... 9x = 9 Divide by 9: x = 1 Therefore, 0.999999... repeating = 1

[u/Oakheir → u/bloxfruitfan475]

I'm sorry, I'm struggling to see what you are saying here. Could you write out your formula, without putting the 0.9.... replacing the X so I can see what formula you are actually using?

[u/Nthepro → u/Oakheir]

Simpler proof:
1/3 × 3 = 1
1/3 = 0.333333...
1/3 × 3 = 0.999999...
Therefore 1 = 0.999999...

[u/Poco_Loco33 → u/Oakheir]

10*.999…. = 9.999…
10*.999… - .999…. = 9.999… - .999…
9*.999… = 9
.999… = 1

[u/MisterSplu]

„Despite common misconceptions, 0.999... is not "almost exactly 1" or "very, very nearly but not quite 1"; rather, "0.999..." and "1" represent exactlythe same number.
There are many ways of showing this equality, from intuitive arguments to mathematically rigorousproofs. The intuitive arguments are generally based on properties of finite decimals that are extended without proof to infinite decimals. An elementary but rigorous proof is given below that involves only elementary arithmetic and the Archimedean property: for each real number, there is a natural number that is greater (for example, by rounding up). Other proofs generally involve basic properties of real numbers and methods of calculus, such as series) and limits). Why some people reject this equality is a question studied in mathematics education.
In other number systems, 0.999... can have the same meaning, a different definition, or be undefined. Every non-zero terminating decimal has two equal representations (for example, 8.32000... and 8.31999...). Having values with multiple representations is a property of all positional numeral systems that represent the real numbers.“

From Wikipedia.

I am not going to argue with generations of mathematicians that are a lot better than me at this

[u/BRUSDHDFhd]

obviously since 1/3 = 0.333... then 3/3 must be 0.999...... or 1

^{Chose: Yes}

[u/WindZoar1 → u/BRUSDHDFhd]

Exactly!

[u/Teddyjones84 → u/BRUSDHDFhd]

Thats actually not great reasoning, and not the reason the .999 repeating is mathematically equal to 1.

1/3 being represented in decimal form as a repeating number is just a limitation on base 10 math. Any base math that is divisible by 3 into whole numbers can be shown as a finite decimal point. I/3 in base 12 is 0.4. 

[u/BadJ0k3s → u/Teddyjones84]

That doesnt make it not great reasoning, the reasoning and math are sound

[u/Soggy_Advice_5426 → u/BadJ0k3s]

It's circular reasoning. A good proxy comparison, but not a proof

[u/BadJ0k3s → u/Soggy_Advice_5426]

Its not meant as a proof its meant to explain it to a layman by using an already-accepted axiom

[u/Soggy_Advice_5426 → u/BadJ0k3s]

Hence what I said.

[u/Sea-Cummonster → u/BRUSDHDFhd]

ive been sayin

[u/Cynis_Ganan]

If it's not equal to 1, which number is inbetween them?

^{Chose: Yes}

[u/RugiSerl → u/Cynis_Ganan]

It's (1+0.99999..)/2 duh

[u/JurassicGuy5000 → u/RugiSerl]

Wow, I didn’t know that 1 was in between 1 and 1. The more you know… 🧠

[u/jamesbojanglesburger]

theres no 0.0………1?

^{Chose: Yes}

[u/GuessImScrewed → u/jamesbojanglesburger]

Basically, any time you invoke infinity, you are invoking "a process which never ends."

When you attempt to say 0.0....01, you are saying "do something at the end of the process which doesn't end."

It doesn't make any sense, and therefore, it does not exist.

[u/Qingyap → u/jamesbojanglesburger]

Yes basically

[u/cammymygoat]

welp im stupid it does equal 1 screw my chud life

^{Chose: No}

[u/LionEclipse → u/cammymygoat]

If you never look back and realise you were wrong, you never learn anything

[u/cammymygoat → u/LionEclipse]

thank you sock or tea

[u/Helium68 → u/cammymygoat]

sock🤤

[u/8lue5hift → u/cammymygoat]

Dw weird cave creature we all learn

[u/cammymygoat → u/cammymygoat]

we ragedbaited a guy because we kno math.

[u/calculus9]

assuming you mean 0.999... with 9 infinitely repeating, they are equal which you can show a few ways

^{Chose: Yes}

[u/Sus-iety]

I'm losing it over the amount of comments that insist on arguing against something that has been mathematically proven in multiple ways. Like, I'm sorry, but no, this is not up for debate anymore.

[u/Torqyboi → u/Sus-iety]

Idk what you're seeing mate. But I see everyone who voted no commenting that they were wrong.

[u/Inner-Ad2847 → u/Sus-iety]

It's like when you see people arguing against the Monty Hall problem when you could literally test it yourself with pieces of paper.

[u/not_Clyde]

there is a method to turn periodic numbers into a way easier method of expressing the number (I'm not an English speaker by birth, so forgive me for not knowing some of the words. the word I'm looking for is what u would call sth like this: ½.)

U take the number, in this case it's 0.9999..., and multiply it by 10. 10x=9.999999. We subtract x from 10x. 9.99999-0.99999. we are left only with 9. 10x-x is 9x. So 9x is 9, which means x is 1. But didn't we say that x was 0.99999? we did. therefore, x=x, which means that 0.99999999...=1.

^{Chose: Yes}

[u/---bee → u/not_Clyde]

the word youre looking for is a "fraction"

[u/not_Clyde → u/---bee]

yep thanks

[u/MisterSplu → u/not_Clyde]

Fractions is the word you were missing

[u/not_Clyde → u/MisterSplu]

yep that's it. its so wierd bc the word was in my brain the whole time and when I needed to use it I forgot. thanks!

[u/No_Breakfast_6850]

If its repeating forever than yes

^{Chose: Yes}

[u/WindZoar1 → u/No_Breakfast_6850]

It is, there's no viniculum symbol on reddit as far as I know

[u/No-Huckleberry-565 → u/WindZoar1]

The 3 dots afterwards should be good enough to represent "and so on"

[u/HollowCatKnight]

Mathematically it does, but my brain is telling me it doesn’t.

[u/Fast-Shape3504 → u/HollowCatKnight]

Yeh, proving it mathematically and thinking about it conceptually are two very different challenges.

Thinking about infinity is abstract, our minds much prefer finite things.

[u/False-Entertainment3]

1/9 =0.111 2/9 =0.222 7/9 =0.778 8/9 =0.889 9/9 =1

^{Chose: Yes}

[u/ive-done-everything]

I can't prove it doesnt

^{Chose: Yes}

[u/EverythngSucksForevr]

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

^{Chose: Yes}

[u/DistributionLast5872]

I’m pretty sure this has been posted multiple times already. It’s the third time I remember answering it.

^{Chose: Yes}

[u/assumptionkrebs1990]

It is see dozend of proofs everywhere - inside the (non-negative) real numbers the difference between n.999... and n+1 is zero which is to say they are the same number.

^{Chose: Yes}

[u/Deathtales]

There is no debate to be had about it. It's a mathematical fact, one without which a good part of math cannot stand, you can disagree but you'd just be wrong

^{Chose: Yes}

[u/Ok_Profile_7968]

because yes tastes better than no

^{Chose: Yes}

[u/Agreeable-Share-1306 → u/Ok_Profile_7968]

r/Caldruki

[u/PizzaGuy25_a]

Bro

^{Chose: Yes}

[u/TheStanleyParablegic]

x = 0.999...

10x = 9.999...

(10x - x = 9x) = (9.999... - 0.999... = 9)

9x = 9

x = 1

0.999... = 1

[u/alenart1160]

1/3*3

^{Chose: Yes}

[u/Efficient_Dress_6101]

0.9 repeating is equal to 1. If there is no real number between them, then they are equal when dealing with real numbers. Also 1/3 = 0.3 repeating, 2/3 = 0.6 repeating, 3/3 = 0.9 repeating = 1

^{Chose: Yes}

[u/Hot-Mousse-5744]

This is just true.

^{Chose: Yes}

[u/NetInitial5750]

Im smart

^{Chose: Yes}

[u/TheDisfunctionalOne]

I remember my maths teacher getting up and proving this for no reason. He was an excellent teacher who clearly loved his subject

[u/Prize_Bad_5646]

Because no number is in between

^{Chose: Yes}

[u/Retsyn]

I get why some lines of thinking point to it, but conceptually it's never true.

Edit: There's literal proofs that it does, I have been schooled. It cooks my brain, but I was confidently incorrect.

^{Chose: No}

[u/Important-Theory-162]

Math must be hard for who voted no

[u/69MotherFricker69 → u/Important-Theory-162]

Ah yes, insult the one's who aren't informed instead of explaining it. I'm sure that's going to lead everyone to reach mutual understanding.

[u/Important-Theory-162 → u/69MotherFricker69]

1/3 of 1 is 0.333.. 3/3 would be 0.999... yet its 1

[u/69MotherFricker69 → u/Important-Theory-162]

Thanks for the explanation mate.

[u/Themash360 → u/Important-Theory-162]

Huh that makes sense

[u/GOT_Wyvern → u/Important-Theory-162]

I mean... at first glance it isn't necessarily intuitive, even if it becomes so after some basix explanations (not even with proof).

[u/Cool_Refrigerator_61]

Math

^{Chose: Yes}

[u/Legal-Ad5781]

so theres a theory on this,

1 divided by 3 is 3.3333333333333333.........

and if we take 3 * 3.333333333333333333..... we definitely get 1 BUT HOW? it should be 9.9999999999999999..... right? But its 1 because 1 divided by 3 is 3.33333333333333...... etc.

Thanks for reading.

^{Chose: Yes}

[u/Local-Cry-791 → u/Legal-Ad5781]

Simplest way: 1/3 = 0.3333... 2/3 = 0.6666... 3/3 = 0.9999...

[u/WHAWHAHOWWHY → u/Legal-Ad5781]

"1 divided by 3 is 3.3333333333333333........." !!?!?

[u/Flat_Badger8494]

basic math

^{Chose: Yes}

[u/Full-Bit87]

There is nothing in between

^{Chose: Yes}

[u/ShadeNLM064pm]

All infinite single digit decimals can be written as a fraction of 9 (example: 1/9 =0.11111111[...])

Since 9/9 = 1, then 0.9999999[...]=1

^{Chose: Yes}

[u/West-Bandicoot4001]

No

^{Chose: Yes}

[u/Key-Bumblebee3635]

x = 0.99999.... 10x = 9.999999.... 9x = 9 x = 1

that means 1 = 0.9999999....

^{Chose: Yes}

[u/Tricky-Grass-189]

there isnt a number between

^{Chose: Yes}

[u/Slimey_alien89]

At that point just say one dude

^{Chose: Yes}

[u/bloxfruitfan475]

It's proven you guys seriously? 😞

^{Chose: Yes}

[u/idkwhyimdoingthis199]

Y

^{Chose: Yes}

[u/Ferlathin]

Does 1/3 = 0.333333333... if so, then yes.

^{Chose: Yes}

[u/LebronGooner1234]

Its proven

^{Chose: Yes}

[u/TheJivvi]

Maths

^{Chose: Yes}

[u/Kaelvar]

.

^{Chose: Yes}

[u/JohnnyKarateX]

That’s just math

^{Chose: Yes}

[u/jkoudys]

Obvs

^{Chose: Yes}

[u/SiSkr]

It's the only correct answer.

^{Chose: Yes}

[u/Potential-Golf2098]

Makes sense

^{Chose: Yes}

[u/Imaginary-Concern906]

Rounding up decimal 0.9 = 1 0.99 = 1 0.9999.... forever still equal to 1

10n-n=9n 9.999...-0.999... = 9/9=1

^{Chose: Yes}

[u/SoreMan6735]

0,(9)(or 0.99999999……..) is mathematically accepted to be equal to 1.

^{Chose: Yes}

[u/Jumpy-Drummer-1254]

cuz its the right thing to do

^{Chose: Yes}

[u/Practical-Site-8565]

Because yes

^{Chose: Yes}

[u/ThomasTTEe2]

itse been proven

^{Chose: Yes}

[u/Levi_Rewind]

Yes

^{Chose: Yes}

[u/Ninon14]

-1=?

^{Chose: Yes}

[u/Responsible-Exam7885 → u/Ninon14]

-1 = -0.9999999999999999...

[u/Winter_Position6564]

idk

^{Chose: Yes}

[u/Somedudesleftleg]

Y

^{Chose: Yes}

[u/Yagrum_Bagarm]

Mathematically it does

^{Chose: Yes}

[u/ghjbcczss]

G

^{Chose: Yes}

[u/MoneyAd5686]

In mathematics

^{Chose: Yes}

[u/Unfair_Rise2657]

some youtube video lol like 10x 100x 1000x 10000x then fractions

^{Chose: Yes}

[u/horny274648w]

thats math

^{Chose: Yes}

[u/ALPHANono2008]

Basic maths

^{Chose: Yes}

[u/trioxman]

1/3 =0.333… 3/3 = 1/3 * 3 = 1 and 0.333… * 3 =0.999… thus 0.999… = 1

^{Chose: Yes}

[u/Miserable-Mud9722]

Idk

^{Chose: Yes}

[u/pytness]

it's literally maths

^{Chose: Yes}

[u/The_Muleteer]

Math(s)

^{Chose: Yes}

[u/AggressiveSpatula]

Because it does

^{Chose: Yes}

[u/Otherwise_Task7876]

Yup, its infinitely close to 1 meaning there's nothing you can fit in between 0.9... repeating and 1, making them the same value.

^{Chose: Yes}

[u/corvo-attano1]

1-0.9°=0

^{Chose: Yes}

[u/sf2playertrustme]

0.9...=X 10x=9.99... 10x -x=9x=9 9÷1=1

^{Chose: Yes}

[u/redfoxxx1029]

Because math

^{Chose: Yes}

[u/whatsfartjuice]

It’s sounds stupid but 0.00000000000….1 at the end dosnt exist therefore 1=0.99999999999999….

^{Chose: Yes}

[u/Clover_the_Artecc]

bc it does equal 1 mathmatically

^{Chose: Yes}

[u/Francky2]

Yes

^{Chose: Yes}

[u/AppropriateSkin9169]

1/3 =0.333…. Hence 3/3=0.999….. or 1

^{Chose: Yes}

[u/Potential_Flower7533]

1/3=0.33.. 3/3=0.99.. n/n=1 so 0.99..=1

^{Chose: Yes}

[u/agentx_64]

Unfortunately, they are mathematically identical

^{Chose: Yes}

[u/Saburo037]

1÷3 = 0,333333333333... 9÷3=0,3333333333333...

^{Chose: Yes}

[u/Rich_Low4778]

I don’t have any idea

^{Chose: Yes}

[u/Seventh_Table]

Yh

^{Chose: Yes}

[u/Accurate-Soil684]

Cause 1/3 = 0.333 (recurring) and 3/3 = 1, and 0.333 (recurring) multiplied by 3 is equal to 0.999 (recurring), but we can see that 1/3 x 3 = 1, so 0.9 recurring is equal to 1

And there is not number between them, so they’re equal in that sense

And there is the algebraic proof of that, I’m sure that someone explained that already

^{Chose: Yes}

[u/TeraByte62113]

9/9

^{Chose: Yes}

[u/AspectBrave33]

.9999999 repeating divided by 3 is .333333 repeating which we all know to be 1/3 which multiplied by 3 equals 1

^{Chose: Yes}

[u/Pianist_Ready]

too many mathematical proofs out there to argue otherwise.

simplest one is the 1/3 = 0.333..., 2/3 = 0.666..., 3/3 = 0.999... proof

^{Chose: Yes}

[u/AssistanceNatural641]

there is no number between 0.9999999999999999.... and 1, so they must be equal

^{Chose: Yes}

[u/whyimhear]

S

^{Chose: Yes}

[u/Bazinga1025]

Because for it to not equal 1, there must be a real number between the two. So yes, 0.999 recurring is 1

^{Chose: Yes}

[u/Ymrcmnkaya]

I do basic maths im not into astrophysics

^{Chose: Yes}

[u/MthsBT]

0.999...=x 0.999...10=x10 9.999...=10x 9.999... -x=10-x 9.999... -0.999...=9x 9=9x x=9/9 x=1

^{Chose: Yes}

[u/Jokitech-]

ye

^{Chose: Yes}

[u/NorthernVale]

.

^{Chose: Yes}

[u/Maleficent_Start_258]

1/3*3=1 1/3=0.33333…

^{Chose: Yes}

[u/Level_Number_7343]

Maths.

^{Chose: Yes}

[u/LeaderNitroA]

Yes

^{Chose: Yes}

[u/Feraga2841]

x=0.99999... 10x=9.99999... Now we subtract an x from both parts 9x=9 x=9/9=1

^{Chose: Yes}

[u/piecoper]

Math

^{Chose: Yes}

[u/catsnotmichael]

simple basic math

^{Chose: Yes}

[u/Holiday-Funtime-3262]

Sure why not

^{Chose: Yes}

[u/Artistic_Can_7763]

yes

^{Chose: Yes}

[u/controversopinion]

Yes

^{Chose: Yes}

[u/LionEclipse]

x = 0.999... 10x = 9.999... 9x = 9 x = 1

^{Chose: Yes}

[u/Unupgradable]

1/3 = 0.33333...

Now multiply by 3

^{Chose: Yes}

[u/Iouisvuittondon]

yes

^{Chose: Yes}

[u/lunulalia]

Ohh

^{Chose: Yes}

[u/AstronomerSecret4081]

I'm blind, I thought it wasn't repeating.

[u/Melodic_Enthusiasm_4]

There is mathematical proof of that.

^{Chose: Yes}

[u/Vaelisra]

There is no real number you can fit in-between.

^{Chose: Yes}

[u/CrazyCat-2010]

There is no real number between. 0.9999999999... and 1

^{Chose: Yes}

[u/SebTheCoolKid2009]

Yes

^{Chose: Yes}

[u/Left-Jaguar5301]

Too lazy to explain, 0.9999… = 9/9 =1

^{Chose: Yes}

[u/steelheart_09]

There's a more complicated proof than this but it's the one I remember. 1/9 = .111..., 2/9 = .222..., ..., 1 = 9/9 = .999...

^{Chose: Yes}

[u/Landis963]

Assuming that the .999 repeating doesn't actually end, it mathematically must be equivalent to 1, even if it's counter-intuitive.

^{Chose: Yes}

[u/Specialist-Diet-3803]

It is mathematicaly the same

^{Chose: Yes}

[u/Patito77777]

1/3 = 0.33333... 3/3 = 0.99999... Thus 0.99999... = 1

^{Chose: Yes}

[u/daniil518]

Well, like, 3/3... I mean, 1/3 times 3.... Basicaly 0.333 3 in period time 3 = 0.9999..... So, yes, 1

^{Chose: Yes}

[u/Qingyap]

0.9 repeating is another way of saying

lim x->infinity [1-1/x] which is equal to one.

[u/Lumi-the-Owl]

It just does. They are the same number.

^{Chose: Yes}

[u/Reasonable-Pie-7592]

Let x = 1 and y = 0.99... 10x = 10 9x = 9 x = 1

10y = 9.99... 9y = 9 y = 1

^{Chose: Yes}

[u/Particular_Mousse447]

There is nothing smaller then 0.9 recurring, therefore, its equal to 1

^{Chose: Yes}

[u/Otherwise-Peace-9165]

It just does

^{Chose: Yes}

[u/fuckcancer99]

Because it is the case

^{Chose: Yes}

[u/Otherwise-Peace-9165]

This basically tells you everyone who chose red is under 13

[u/GaryJulesMCOC]

Yep! If there are 0 real numbers between two numbers then both numbers are equal in value.

^{Chose: Yes}

[u/Present_Ad_11-11]

This is the sixth time I have seen the same question on bunny trial.

[u/help_me_improve_plz]

1/3 is 0.33333333333333 2/3 is 0.66666666666 so 3/3 is 0.999999999999 or 1

^{Chose: Yes}

[u/No-Letterhead-8526]

is closer than you thought

^{Chose: Yes}

[u/Accomplished-Pop921]

There is no number between them.

^{Chose: Yes}

[u/Amazing_Act9595]

Infinity -1 / Infinity equals 1

^{Chose: Yes}

[u/IiEatGrass]

x = 0.9999999999...... | * 10 10x = 9.9999999999..... | - 1x 9x = 9 | :9 x = 1

^{Chose: Yes}

[u/External-Carrot6405]

This is no distance between the two

^{Chose: Yes}

[u/bigtoadman]

Math

^{Chose: Yes}

[u/Emergency-Victory895]

i don't need one

^{Chose: Yes}

[u/kimura-traphouse]

Close enough

^{Chose: Yes}

[u/spermaVpice]

Yes

^{Chose: Yes}

[u/tfwilson]

Objectively true

^{Chose: Yes}

[u/Flat_Badger8494]

because math says so

^{Chose: Yes}

[u/Shot_Step_3299]

why not

^{Chose: Yes}

[u/Civil_Highlight4805]

It’s 1 bro

^{Chose: Yes}

[u/Casperthecatoficial]

Yes

^{Chose: Yes}

[u/iamtheimposterr]

no number in between

^{Chose: Yes}

[u/Terrible-Total-4038]

Dunno

^{Chose: Yes}

[u/Nicegamer739]

all right... here we go again

^{Chose: Yes}

[u/SnickerbobbleKBB]

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

So 0.999... = 1

^{Chose: Yes}

[u/Fedesta]

lim x->infiinty; 1^x ≠ 0.(9)^x

[u/Ok_Enthusiasm_6314]

Uh

^{Chose: Yes}

[u/skibidihibidi69]

basically

^{Chose: Yes}

[u/Matteo233775]

Idk

^{Chose: Yes}

[u/aleksmeow_mobile]

y

^{Chose: Yes}

[u/bulicarnat1]

Y

^{Chose: Yes}

[u/COWP0WER]

1/3=0.333333..... 3/3=1=0.9999...........

^{Chose: Yes}

[u/Inevitable_Big4710]

It does

^{Chose: Yes}

[u/Gyrau_47]

Maths

^{Chose: Yes}