Does 0.9 Repeater = 1?

Pages: 1 2 3 4 5

Index »
Community »
Debate and Serious Talk »
Does 0.9 Repeater = 1?

2008-02-07 21:26:06

weasel_thingo: Member; +74|6596

tazz. wrote:
Does 0.9 Repeater = 1?

I have the following to back it up....

1/3 = 0.3(repeater) correct? correct.

2/3 = 0.6(repeater) correct? correct.

3/3 = 0.9(repeater) correct? exactly.

As you can see i have followed a pattern, thus we know 3/3 = 1, but alas, why not 0.9(repeater)?

1/3 does not = 0.3(repeat)
0.3 is just the closest you can get, using that to prove 0.9=1 is fail

2008-02-07 21:30:09

SenorToenails: Veritas et Scientia; +444|6400|North Tonawanda, NY

weasel_thingo wrote:
1/3 does not = 0.3(repeat)
0.3 is just the closest you can get, using that to prove 0.9=1 is fail

1/3 does equal .333...

It does this for all the same reasons that .999... = 1.

This is a non-issue for anyone who studies mathematics.

2008-02-07 21:39:02

Hakei: Banned; +295|6265

SenorToenails wrote:
Hakei wrote:
Vilham wrote:
Indeed it does. Btw REOCCURRING not repeater.
I always thought it was 'recurring'.

Also; if this statement is true then please explain this.

If 1=0.999... Then:

1-0.999... = 0.
0 = (1/10)*(1/10)*(1/10)...
1-0.999 = 1-(0.9)-(0.09)-(0.009) Which is equal to 1/10/10... = (1/10)*(1/10)*(1/10)...

So now we know that 0 is equals to (1/10)*(1/10)*(1/10)...

We can say that 1/10^N=0
So...

0x10^n = 1
0 = 1.
Honestly, I don't have any idea of what you are doing here, but zero times anything is zero.

I'm saying if what is being said is true, 0 = 1.

Therefore, it seems like it doesn't work, unless you can prove that 0=1.

2008-02-07 21:39:49

usmarine: Banned; +2,785|7031

lulz

2008-02-07 21:52:53

SenorToenails: Veritas et Scientia; +444|6400|North Tonawanda, NY

Hakei wrote:
I'm saying if what is being said is true, 0 = 1.

Therefore, it seems like it doesn't work, unless you can prove that 0=1.

I see what you are saying, and what you are saying is wrong.

(1/10)^N != 0, because it is technically the limit as N->infinity (1/10)^N = 0. There is a large difference.

Look at it this way, .999... is equivalent to $https://upload.wikimedia.org/math/5/7/8/578c588335106e68a836c53c959c461d.png$ which is equivalent to 1.

Just read this article. It explains the whole thing. This forum does not have a LaTeX interpreter, so I cannot explain this clearly and easily. It is your understanding of what .999... means is what is confusing you.

Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal."
Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.
Some students interpret "0.999…" (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity".
Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since a sequence need not reach its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999…" as meaning the sequence rather than its limit.
Some students regard 0.999… as having a fixed value which is less than 1 by an infinitely small amount.
Some students believe that the value of a convergent series is an approximation, not the actual value.

Last edited by SenorToenails (2008-02-07 22:28:43)

2008-02-07 22:01:54

{M5}Sniper3: Typical white person.; +389|7030|San Antonio, Texas

3/3 = 1, no matter how you slice it.

2008-02-07 22:03:36

Shaguart: Titties; +56|6639|Calgary, Canada

My math teacher once told us about this
he said it does equal one so...
IT DOES

2008-02-07 22:19:26

Hakei: Banned; +295|6265

SenorToenails wrote:
Hakei wrote:
I'm saying if what is being said is true, 0 = 1.

Therefore, it seems like it doesn't work, unless you can prove that 0=1.
Any attempt to make 0=1 is a logical fallacy.

You assert that 0 multiplied by 10 raised to some N equals 1. That is false.

And the whole point I said that was because I was using the theory that 1 = 0.9999.

If 1 is equal to 0.999... then 1 minus 0.999... is equal to 0 correct?

So 1 - (0.9) - (0.09) - (0.009)... = 0 correct?

So 0 + (0.9) + (0.09) + (0.009) = 1

So now by this theory (1/10)*(1/10)*(1/10) = 0. Right?

So (1/10)^N = 0.

Z/Y = X, which leads to X x Y = Z.

So 0 X 10^N = 1. (0.999...)

0 X anything is 0, so it can't equal 1.

2008-02-07 22:22:24

G3|Genius: Pope of BF2s; +355|6896|Sea to globally-cooled sea

Fractions are always a more accurate way to represent a number that is not a whole number.

representing pi as 22/7 will always get you a more accurate answer than using 3.14159 etc..

the only reason we use decimals is because until the graphing calculator, the quickest way for electronic calculations was to convert to a decimal and punch it into your calculator.

When I was in high school we were required to get a TI-82 or better, so I had a TI-83 calculator, and that would allow me to use fractions rather than decimals when computing.

I suppose it's an interesting argument, but ultimately it's pointless because it simply comes down not to arithmetic specifically, but to a weakness in our system for representing a number.

2008-02-07 22:32:41

SenorToenails: Veritas et Scientia; +444|6400|North Tonawanda, NY

G3|Genius wrote:
Fractions are always a more accurate way to represent a number that is not a whole number.

representing pi as 22/7 will always get you a more accurate answer than using 3.14159 etc..

the only reason we use decimals is because until the graphing calculator, the quickest way for electronic calculations was to convert to a decimal and punch it into your calculator.

When I was in high school we were required to get a TI-82 or better, so I had a TI-83 calculator, and that would allow me to use fractions rather than decimals when computing.

I suppose it's an interesting argument, but ultimately it's pointless because it simply comes down not to arithmetic specifically, but to a weakness in our system for representing a number.

No. You are so wrong that it isn't even funny.

Pi is an irrational number. It cannot be described by a fraction. And when using a computer to solve a problem, the decimal of pi out to machine precision will get a much more accurate answer than 22/7 will. 22/7 is simply an approximation.

The simple fact is that there are numbers which cannot be described as a fraction. There is no weakness in the system of representing numbers. The weakness lies in people not understanding the way numbers are represented.

2008-02-07 22:35:36

G3|Genius: Pope of BF2s; +355|6896|Sea to globally-cooled sea

really? I was taught that pi is 22/7. I'm going to look it up, because now I feel like what little math i understood is all now imaginary!

2008-02-07 22:38:56

SenorToenails: Veritas et Scientia; +444|6400|North Tonawanda, NY

Hakei wrote:
SenorToenails wrote:
Hakei wrote:
I'm saying if what is being said is true, 0 = 1.

Therefore, it seems like it doesn't work, unless you can prove that 0=1.
Any attempt to make 0=1 is a logical fallacy.

You assert that 0 multiplied by 10 raised to some N equals 1. That is false.
And the whole point I said that was because I was using the theory that 1 = 0.9999.

If 1 is equal to 0.999... then 1 minus 0.999... is equal to 0 correct?

So 1 - (0.9) - (0.09) - (0.009)... = 0 correct?

So 0 + (0.9) + (0.09) + (0.009) = 1

So now by this theory (1/10)*(1/10)*(1/10) = 0. Right?

So (1/10)^N = 0.

Z/Y = X, which leads to X x Y = Z.

So 0 X 10^N = 1. (0.999...)

0 X anything is 0, so it can't equal 1.

See the bolded part above? That is wrong.

$https://upload.wikimedia.org/math/a/3/7/a370a49aad105b87eaf3e0dbc66acadc.png$

That is the proper way to decimal representation.

2008-02-07 22:39:21

CoronadoSEAL: pics or it didn't happen; +207|6788|USA

disagree. the wording is touchy.

1/3 does not equal .333
it is just an ESTIMATION of 1/3

don't use estimations (like 22/7 for pi) when calculating anything you want exact.

2008-02-07 22:41:07

SenorToenails: Veritas et Scientia; +444|6400|North Tonawanda, NY

G3|Genius wrote:
really? I was taught that pi is 22/7. I'm going to look it up, because now I feel like what little math i understood is all now imaginary!

Pi:

3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 626945604241965285022210661186306744278622039194945047123713786960956364371917 287467764657573962413890865832645995813390478027590099465764078951269468398352 595709825822620522489407726719478268482601476990902640136394437455305068203496 252451749399651431429809190659250937221696461515709858387410597885959772975498 930161753928468138268683868942774155991855925245953959431049972524680845987273 644695848653836736222626099124608051243884390451244136549762780797715691435997 700129616089441694868555848406353422072225828488648158456028506016842739452267 467678895252138522549954666727823986456596116354886230577456498035593634568174 324112515076069479451096596094025228879710893145669136867228748940560101503308 617928680920874760917824938589009714909675985261365549781893129784821682998948 722658804857564014270477555132379641451523746234364542858444795265867821051141 354735739523113427166102135969536231442952484937187110145765403590279934403742 007310578539062198387447808478489683321445713868751943506430218453191048481005 370614680674919278191197939952061419663428754440643745123718192179998391015919 561814675142691239748940907186494231961567945208095146550225231603881930142093 762137855956638937787083039069792077346722182562599661501421503068038447734549 202605414665925201497442850732518666002132434088190710486331734649651453905796 268561005508106658796998163574736384052571459102897064140110971206280439039759 515677157700420337869936007230558763176359421873125147120532928191826186125867 321579198414848829164470609575270695722091756711672291098169091528017350671274 858322287183520935396572512108357915136988209144421006751033467110314126711136 990865851639831501970165151168517143765761835155650884909989859982387345528331 635507647918535893226185489632132933089857064204675259070915481416549859461637 180270981994309924488957571282890592323326097299712084433573265489382391193259 .... and so on

2008-02-07 22:42:10

SenorToenails: Veritas et Scientia; +444|6400|North Tonawanda, NY

CoronadoSEAL wrote:
disagree. the wording is touchy.

1/3 does not equal .333
it is just an ESTIMATION of 1/3

don't use estimations (like 22/7 for pi) when calculating anything you want exact.

NO!

.333333->taken to inifinite decimals of 3 is the decimal representation of 1/3. It is NOT an "estimation".

2008-02-07 22:43:46

G3|Genius: Pope of BF2s; +355|6896|Sea to globally-cooled sea

dammit, you're right.

wtf.

anyway, in case you were wondering, this is why: $https://upload.wikimedia.org/math/e/b/b/ebbc7d730ea3edaa29c3dd0b037688d5.png$ lol

fuck that I'm gonna go read some calvin and hobbes

2008-02-07 22:49:24

CoronadoSEAL: pics or it didn't happen; +207|6788|USA

SenorToenails wrote:
CoronadoSEAL wrote:
disagree. the wording is touchy.

1/3 does not equal .333
it is just an ESTIMATION of 1/3

don't use estimations (like 22/7 for pi) when calculating anything you want exact.
NO!

.333333->taken to inifinite decimals of 3 is the decimal representation of 1/3. It is NOT an "estimation".

i see your point, but it still doesn't make any sense.
where'd the rum .00000001 go if .333 is taken to infinity?
so then how can it be a representation and not an estimation?

Last edited by CoronadoSEAL (2008-02-07 22:51:32)

2008-02-07 22:59:12

SenorToenails: Veritas et Scientia; +444|6400|North Tonawanda, NY

CoronadoSEAL wrote:
i see your point, but it still doesn't make any sense.
where'd the rum .00000001 go if .333 is taken to infinity?
so then how can it be a representation and not an estimation?

The point is that it is taken to infinity so there is no remaining portion of the number.

Thus the representation with limits.

2008-02-08 01:02:40

Gamematt: Stocking ur medpacks; +135|6932|Groningen, The Netherlands

SenorToenails wrote:
Gamematt wrote:
As soon as you go near infinite numbers math fails.

My math teacher told me a cool story once, lets see if I can reproduce it...:

It went something like, somewhere in the galaxy there is this train. And it has a infinite number of carriages.

Every carriage contains 1 person, the train is full. (small carriages)

The train rolls into a station and the driver asks everybody to look at their carriage number, multiply it by 2 and go sit in that particular carriage.

1 ---> 2
3 ---> 6
10 ---> 20
500 ---> 1000 etc...

-the train didn't get any longer
-nobody left the train

and still the train suddenly is half empty =0
all the uneven carriages are empty

/fail
the story sounds really dull like this
Woohoo, countable infinity. Math does not break with numbers approaching infinity. It just get more complicated.

Tell me about it, I hated the exams on this subject 0.o
I'm good at maths but not that good

2008-02-08 21:11:24

tazz.: oz.; +1,338|6444|Sydney | ♥

Ok....

I aggree with most of what is happening...

Hakie... Your making it more complicated than it has to be....

I AGGREE, 1/3 DOES NOT = 0.3(RECURRING***)

Nothing to the fraction of a third, can be made into an [b]ACCURATE[b] Decimal...

I was meerly pointing out the fact, that common society, accepts that it can be a decimal, although it cannot... and thus, playing around with the fact that 0.9(recurring...) is 1

^{everything i write is a ramble and should not be taken seriously.... _{seriously. ♥}}

2008-02-08 21:17:59

Skorpy-chan: Member; +127|6615|Twyford, UK

No. 0.99 recurring equals 0.99 recurring. It's nearly 1, but not.

2008-02-08 22:08:23

CoronadoSEAL: pics or it didn't happen; +207|6788|USA

exactly what i was saying.

SenorToeNails, refute the last few posts please.

2008-02-08 22:36:55

topal63: . . .; +533|6988

CoronadoSEAL wrote:
exactly what i was saying.

SenorToeNails, refute the last few posts please.

You're thinking about it the wrong way, IMO.

You think there is an infinitesimal (<-- an infinitely small number), other people have argued for their existence, but they just don't exist. And there is no real rigorous proof for them either + they are axiom dependent. Meaning they are definition dependent; unless & until you assume they exist and then rationalize their existence they don't exist. So why conjure such nonsense up?

You more or less thought of a number 0.00001 in your mind & that some where there's a small difference. But this is utterly wrong. You're not thinking of a number, that is your error. You should try and think of a logical representation for an idea instead.

Write it like this instead 0.000...01, what does the ellipses represent in this case; it represents infinity. So what is the value of the 01 part after infinity; an infinite expansion. As the expansion gets larger the value approaches zero. As an infinite expansion :: it equals absolutely nothing. It is zero.

0.00000...0 = 0.00000...01, seems strange at first but it isn't. And 0.999... = 1.

0.0...01
0.00...01
0.000...01
0.0000...01
0.00000...01 (it is getting smaller upon expansion, at infinity it equals zero) = 0

It is an infinite expansion that certainly resolves at being equal to zero. The ...01 part is non-existent, as the expansion is resolved at infinity. It is nearly the same idea as a limit in calculus.

0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 + 0.000009... is just an algebraic expansion of the number 1 (with the ellipses representing the infinite expansion, and the Summation symbol not being shown).

0.9999... is just a condensed version of the algebraic expansion of the number 1. The sum resolves as the expansion approaches infinity to be exactly equal to 1.

Last edited by topal63 (2008-02-08 22:59:56)

2008-02-08 22:42:19

Blehm98: conservative hatemonger; +150|6733|meh-land

.999 with an infinite number of 9s can be assumed to be infinitely close to 1...

you can assume it to be one under any circumstance because under any restrictions, you can drag out the 9s far enough so as to make any error more minor that is feasible in the universe anyway. If you have .9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 of anything, the error caused by rounding it to 1 is less than any registerable amount any way

i guess that's a simple way of putting it...

2008-02-08 22:52:55

topal63: . . .; +533|6988

Blehm98 wrote:
.999 with an infinite number of 9s can be assumed to be infinitely close to 1...

you can assume it to be one under any circumstance because under any restrictions, you can drag out the 9s far enough so as to make any error more minor that is feasible in the universe anyway. If you have .9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 of anything, the error caused by rounding it to 1 is less than any registerable amount any way

i guess that's a simple way of putting it...

It is not assumed to be equal to 1. It is not almost equal to 1.

It is equal to 1.

Pages: 1 2 3 4 5

Index »
Community »
Debate and Serious Talk »
Does 0.9 Repeater = 1?

Board footer

Jump to

BF2S Forums Does 0.9 Repeater = 1?

tazz. wrote:

weasel_thingo wrote:

SenorToenails wrote:

Hakei wrote:

Vilham wrote:

Hakei wrote:

SenorToenails wrote:

Hakei wrote:

G3|Genius wrote:

Hakei wrote:

SenorToenails wrote:

Hakei wrote:

G3|Genius wrote:

CoronadoSEAL wrote:

SenorToenails wrote:

CoronadoSEAL wrote:

CoronadoSEAL wrote:

SenorToenails wrote:

Gamematt wrote:

CoronadoSEAL wrote:

Blehm98 wrote:

Board footer