View Full Version : 1/3 + 2/3 =/= 1

Miguel

09-30-2005, 02:29 PM

1/3 = .33333333333333333333333~

2/3 = .66666666666666666666666~

.: 1/3 + 2/3 = .99999999999999999~

.9999999999999~ =/= 1

discuss :eek:

Waterwings

09-30-2005, 02:34 PM

LOL good call, Go post it on a Mensa forum:D

AMG_POWER

09-30-2005, 02:41 PM

i dont care.

Raging Lamb

09-30-2005, 02:45 PM

close enough to 1.

King Luis

09-30-2005, 02:52 PM

it depends on what you are doing....if it's something that need very great precision then 0.9999999~ but if it's just something general 1.

SebSter

09-30-2005, 02:55 PM

no no. 0.999999~ = 1. not "close enough". they are absolutely equal. and what miguel posted is one of the proofs.

edit: here it is in more of a rough proof form

1/3 = .33333333333333333333333~

2/3 = .66666666666666666666666~

.: 1/3 + 2/3 = .99999999999999999~

but 1/3 + 2/3 = 3/3 = 1

.: .99999~ = 1

Veemax

09-30-2005, 03:15 PM

1/3 + 2/3 = 3/3

3/3 = 1

2 = 1+1

2+2=4

4=2+2

235698x3.67895=867121.15

867121.15 = a nice annual salary :o)

King Luis

09-30-2005, 03:22 PM

fractions and decimals are two different types of numbers.

moregothanshow

09-30-2005, 03:28 PM

i will be accepting donations of .9999999~ from all members as of now

Thanks!

Waterwings

09-30-2005, 03:36 PM

.999999999999~ approximatly equal to one (can't make the damn sign on a keyboard) would that be true. Cause it really isn't one

niko_gt

09-30-2005, 03:46 PM

.99999999~ is an estimated # on a calculator screen, it divides into itself ovre and over again, i cant remember the proper term for it, as i forget everything i learned in highschool, ok i dunno what im talking about. i give up

sirex

09-30-2005, 03:56 PM

2/3 = 0.66666666666666666666666666666667

1/3 = 0.33333333333333333333333333333333

= 1

your calculator is a peice of shit.

OH yeah also....

if we go miguels way.. you are missing significant digits..

1/3 + 2/3 = 1 because 0.99999999 rounds up to 1 as you can only have 1 significat digit in your answer.

2slow2race

09-30-2005, 03:56 PM

your all on acid!

especially miguel. *th-up*

Miguel

09-30-2005, 04:15 PM

2/3 = 0.66666666666666666666666666666667

1/3 = 0.33333333333333333333333333333333

= 1

your calculator is a peice of shit.

OH yeah also....

if we go miguels way.. you are missing significant digits..

1/3 + 2/3 = 1 because 0.99999999 rounds up to 1 as you can only have 1 significat digit in your answer.

"rounds up" is another way of saying NOT EXACTLY EQUEL.

Miguel

09-30-2005, 04:17 PM

fractions and decimals are two different types of numbers.

a number is a number.

1/3 and the decimal version are intended to be exact representations of each other.

Math is all a lie.... all my profs were liars.. what in the **** was I thinking doing advanced calc and algebra in university

:(

Raging Lamb

09-30-2005, 04:21 PM

Your baby has a beautiful eye.

sirex

09-30-2005, 04:25 PM

Im not an expert on significant digits, I can tell you that...

however, your answer cant be more then 1 number.

and saying your final answer is 0.9 is not accurate either.

Thefore since we can only be as accurate as 1 number placement you have to use significant digits

0.99999999999 when dividing 1/3 + 2/3 = must equal 1x10^0 or 1

or

0.33333333 = 3.0x10^-1

0.66666666 = 7.0x10^-1

when added its 1.0

SebSter

09-30-2005, 04:26 PM

I think you guys are missing the point here.

0.9999~ = 1

There is no maybe about it, its not an approximation, it is a mathematical fact.

Ok, here's a much more elementary way so you can see it:

1/9 = 0.111111~

2/9 = 0.222222~

3/9 = 0.333333~

4/9 = 0.444444~

5/9 = 0.555555~

6/9 = 0.666666~

7/9 = 0.777777~

8/9 = 0.888888~

9/9 = ?

sirex

09-30-2005, 04:43 PM

bah.. I dont know how else to explain it.. and i realise with significant digits it is rounding... but like stated earlier you cant mix fractions with decimals as its not the same..

The point is you can never split a pie 3 ways evenly. There will always be a tiny percentage more going to one person the the rest. IT has to be that way.

As you said when you add it up it comes to

0.999999999999999999999999999999999999998 or whatever it is. well tahts the point it keeps going forever because the pieces that you cut are not exact.

You cant cut the peice Exactly to be 1/3 of a full pie..

you are cutting it to be

0.333333333333333333333333333333333333333333333333 3333333333333333 and the number continuous.

I really dont see what is so hard to grasp about this concept.

SebSter

09-30-2005, 04:52 PM

^

Well for one the fact that you can cut a pie in three equal sizes. 120 degree angles from the center. (A perfect circle can be split into three equal pieces.)

sirex

09-30-2005, 05:32 PM

"Well for one the fact that you can cut a pie in three equal sizes. 120 degree angles from the center. (A perfect circle can be split into three equal pieces.)"

Well if this is true then why doesn't adding 2/3 + 1/3 (the decimal points) = 1?

By what you are saying 120 degrees is 1/3 of 360.. And it is exactly 1/3 of 360 then why doesn't this hold true for the fractions?

Angle measurement is based off pie, radians and all that other fun stuff. And no you cant cut a pie into 3 equally sized pieces.

BECAUSE one piece will have to be of greater or lesser value then the other peices to fit.

not

1 divided by 3 is = 0.333333333333333333333333333333333333333333333333 33

+

1 divided by 3 is = 0.333333333333333333333333333333333333333333333333 33

+

1 divided by 3 is = 0.333333333333333333333333333333333333333333333333 33

=0.99999999999999999999999999999999999999999999999 999

These numbers all continue indefinately

SebSter

09-30-2005, 05:43 PM

No man thats what youre not getting. Adding the decimals for 2/3 (0.666~) and 1/3 (0.333~) DOES = 1.

0.99999 continued indefinately EQUALS exactly 1. Its a simple mathematical fact. There is no maybe about it, there is no doubt about it, there is no approximation.

Fractions and decimals are NOT different things, they are different ways of representing the SAME thing. This isnt a debate, there is NO chance for difference of opinion here. Its a mathematical fact that 0.999~ = 1. To disagree with it would be to disagree that 1+1 = 2.

(And as for the pie example. I dont know who told you that it cant be cut into three equal pieces, because it can. From the center of the circle draw out lines to the end 120 degrees apart from eachother, and you will have 3 equal pieces, not slightly equal, not almost equal... EXACTLY equal.)

///m powered

09-30-2005, 05:45 PM

Hmmm...

http://img84.imageshack.us/img84/7537/163172413685hf6vo.gif

sirex

09-30-2005, 05:50 PM

0.99999 continued indefinately EQUALS exactly 1. Its a simple mathematical fact. There is no maybe about it, there is no doubt about it, there is no approximation.

(And as for the pie example. I dont know who told you that it cant be cut into three equal pieces, because it can. From the center of the circle draw out lines to the end 120 degrees apart from eachother, and you will have 3 equal pieces, not slightly equal, not almost equal... EXACTLY equal.)

Seems like an aproximation to me. How is 0.9999999999999999 = 1 unless you round up.

Yeah you can have 3 pieces that are all equal

.33333333333333333333333333333333333333

.33333333333333333333333333333333333333

.33333333333333333333333333333333333333

but they dont add up to one. They add up to .999999999999999999999999

and as miguel stated thats not 1. Why is that.

SebSter

09-30-2005, 05:52 PM

Once again. It IS 1. What can't you understand about that? (0.999 repeating IS 1. They are absolutely equal.)

Miguel is just being a goof.

SebSter

09-30-2005, 05:56 PM

Here: http://www.mathmojo.com/interestinglessons/999repeating/999repeating.html

Enjoy

Raging Lamb

09-30-2005, 05:57 PM

Yeah you can have 3 peices that are all equal

.33333333333333333333333333333333333333

.33333333333333333333333333333333333333

.33333333333333333333333333333333333333

but they dont add up to one. They add up to .999999999999999999999999

and as miguel stated thats not 1. Why is that.

Wow I have a few questions for you:

what's 1-1?

and if I buy something for $1, am I really paying $0.99999999?

Is 2 = 1.99999...(infinite repitition)..8?

What about 1,000,000,000,000,000,000?

I'm so confused :confused:

sirex

09-30-2005, 06:03 PM

I dont get it.

no if we say its 1.00$ we are defining it as EXACTLY 1.00 too exaclty 3 significant digits. Another item can be 0.99 cents which again we have defined with 2 significant digits. These are exact figures.

but my point is 0.999999999999999999999999999999999999999999999 (repeating to inifinite decimal places) Means it never ends and thus there is no way to give it a final value of exactly 1.00 as it is .9999999999999999999999 repeating.

Raging lambs, if you buy 3 products that are all 33 cents each does it become a dollar?

33 cents times 3 is 99cents.

All this time I thought I was trying to defeat what miguel was saying but now I realse how right he is..

This is a load of shit. HOW is it ONE? 1.00000000000

This makes no sense.

0.999999999999999999999

Is not 1 as it is is

0.000000000000000000001 of a number off. Althugh very small in error It is missing that value.

Fck take 100 pennies and play around with it.. YOU DONT get 1 dollars with 99 pennies. You get 99 cents.. Fusjdfgbas'dfnas'vnas'

i hate math and numbers.

And this whole degrees thing is bullshit too.

120 degrees of a circle is giving it a rounded digit.

(2(pi)) / 3 = 120 degrees

but circles are based of pi.

Pi:

Mathematics. A transcendental number, approximately 3.14159, represented by the symbol, that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions

This alone disproves that your circle cannot cut a piece out of your circle to exactly 120 degrees because it is an aproximation of the ratios.. skaodhfa'shdf

Here is pi to 1000 decimal places:

3. 14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31859 50244 59455 34690 83026 42522 30825 33446 85035 26193 11881 71010 00313 78387 52886 58753 32083 81420 61717 76691 47303 59825 34904 28755 46873 11595 62863 88235 37875 93751 95778 18577 80532 17122 68066 13001 92787 66111 95909 21642 01989 ...

**** it, if I am wrong I dont care. But Im with Miguel This is stupid and garbage, and lies!

SebSter

09-30-2005, 06:12 PM

Raging Lamb is just playing dumb..lol, Im pretty sure he gets it. Sirex, you're still not understanding it.

1/3 does not equal 0.33, or 0.333. It equals 0.33333333 repeating infinitely.

You get 1/3 = 0.333333(infinitely repeating)

- multiply both sides by 3.

You get 3/3 = 0.9999999(infinitely repeating)

Trust me, being forced to take first year calculus this shit got drilled into my head.

0.9 does not equal 1

0.999 does not equal 1

0.999999(inifinitely repeating) does equal 1. end of story!

Raging Lamb

09-30-2005, 06:14 PM

So again, 1 - 1 =/= 0

it's '0.000..(repating infinitely)..0001'. and if you subtract this number from itself, you still won't get 0.

Therefore I just proved that 0 does not exist.

Call the army!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

sirex

09-30-2005, 06:15 PM

No no I get it.. But now that I do get it, I just dont want to beleive it! lol.. ****en calculus. Im in calculus too, Im just not there yet.

Raging Lamb

09-30-2005, 06:16 PM

I'm not 'playing' stupid, it's a permanent condition :(

Miguel

09-30-2005, 09:53 PM

So again, 1 - 1 =/= 0

it's '0.000..(repating infinitely)..0001'. and if you subtract this number from itself, you still won't get 0.

Therefore I just proved that 0 does not exist.

Call the army!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

*uzi*

Miguel

09-30-2005, 09:56 PM

No no I get it.. But now that I do get it, I just dont want to beleive it! lol.. ****en calculus. Im in calculus too, Im just not there yet.

so if 1 doesnt exist and 0 doesnt exist then binary must be a lie as well.

Think about it.

http://www.7art-screensavers.com/screens/3d-matrix/matrix-3d-neo-screensaver.jpg

windsor318is

09-30-2005, 10:24 PM

What!!!!!!!!!!!!!!!

from what i was taught, fractions and decimals aren't equal.

*********1/3 is more accurate than .3333333333~************

.33333333~ is infinitately repeated because 1/3 isn't divisible.

mkgino

10-01-2005, 12:06 AM

http://img265.imageshack.us/img265/8281/accomadator6cj3dz.gif roffle roffle roffleroffle roffle roffleroffle roffle roffleroffle roffle roffleroffle roffle roffleroffle roffle roffle

mkgino

10-01-2005, 12:09 AM

OGMZ CaRRoT tawP !!!1

http://img265.imageshack.us/img265/4272/ctopworkout21ns.jpg

M3ti Compact

10-01-2005, 12:09 AM

+1...

opps, I mean

+0.9999999999999999999999999999999

mkgino

10-01-2005, 12:14 AM

http://img120.imageshack.us/img120/7273/picse126wv.jpg

1/3 = .33333333333333333333333~

2/3 = .66666666666666666666666~

.: 1/3 + 2/3 = .99999999999999999~

.9999999999999~ =/= 1

discuss :eek:

The logic is fine right up to the last equation, which is crap. .99 repeated is not a rational number therefore you can't think of it as being a bunch of 9's. It doesn't end. Here: 1=9/9=0.9+0.9/9=0.99+0.09/9=0.999+0.009/9= ... =0.999999999999999999999999999 + 0.000000000000000000000000009/9...

You can keep dividing out till infinity. The limit of the right term is 0, and of the left is 1. But it will never happen! Infinity's a bitch. Now go rest your brain.

M3ti Compact

10-01-2005, 12:25 AM

ok, serious now.

The reason why you get 0.999 is as stated above, you converted a fraction into a decimal. Your not comparing the same things. Why? Try it out yourself. Put in 0.33333 + (2/3) in your calculator.

In the fraction (1/3), the resulting decimal 3's go to infinity, when you enter it into your calculator, it is just like turning 0.33333~ into 0.3333300000. So, right off the bat, when you converted from fraction into decimal, in this case, your missing 0.00000333333~

Same thing when you convert (2/3) into decimal, the resulting 6's go to infinity. Your supposed to have 0.66666~, but instead you got 0.6666600000, so your missing 0.00000666666~

Add up your missing numbers, 0.00000333333 + 0.00000666666, and you get your missing 0.000099999, which can be rounded to 0.00001.

mkgino

10-01-2005, 05:04 AM

fsdajfosafjdsafsajf

BMW_7

10-02-2005, 01:02 AM

I ****ING HATE MATH lc

moregothanshow

10-02-2005, 01:45 AM

numbers are bulshit, this can be debated forever, its what u were taught, and by whom. eg. i am brought up to think that a girl that looks like liza minelli is hot therefore if i see a girl that looks like liza i would say damn she hawt!, on the other hand i was taught liz hurly is the shit and will always be the best model ever, then when i see a girl that looks like her she is hot. same thing applies: the digit 1 can be equal to .999999~ or it can not be, it really depends on "your school of thought" at the end of the day if the government thought u owed them .9999999~ of a cent they would hunt u down for that 1 cent ;)

SebSter

10-02-2005, 03:01 PM

^its not a matter of debate. it has nothing to do with how you are brought up to think. mathematical facts are absolute.

it is not debatable that 1 + 1 = 2. just like it is not debatable that 0.999~ = 1. ask any professor or expert of mathematics. there is no matter of opinion, its undeniable fact.

Raging Lamb

10-02-2005, 04:27 PM

I've submitted a link to this page to the 'Mathematical Association of America' (link (http://www.maa.org/)).

We should all be famous soon *th-up*

propr'one

10-02-2005, 07:34 PM

you guys are all retards

moregothanshow

10-03-2005, 02:57 AM

^its not a matter of debate. it has nothing to do with how you are brought up to think. mathematical facts are absolute.

it is not debatable that 1 + 1 = 2. just like it is not debatable that 0.999~ = 1. ask any professor or expert of mathematics. there is no matter of opinion, its undeniable fact.

its not undeniable fact, it's a fact a few ppl decided that thats whats gonna be. just like how some ppl decided the earth/humans came to be 2000 years ago. numbers are decided representations of what "we" perceive as a means to communicate. lets take for example this character here in the quotations "3", what if i decided that that character is the representation of a cow and i asked my fellow villagers if this was a good idea, eventually everyone accepted that that symbol would be a cow, take a wild guess what they would do if u said u would give them a 3 for free?!?

Miguel

10-05-2005, 11:18 PM

why is this in the recycle bin?

moregothanshow

10-05-2005, 11:19 PM

because the threads u start are always trouble!! hahaha!

Justin e36

10-08-2005, 09:06 PM

this thread was actually getting some good responses... shame to see it in the recycle bin.

Raging Lamb

10-08-2005, 09:19 PM

people don't like math.

propr'one

10-09-2005, 01:27 AM

meh fundamentally flawed. 0.99999999~ isn't 1. but technically, 1/3 isn't 0.333~ if we talk in terms of rational numbers, even if we go to 100 digits past zero, 10 can't get split up into 3 evenly, aka to split up 10 into 3 different sums you'd have 3+3+4=10. so 1/3+2/3's DOES equal 1, but 1/3=/= 0.333~

:D

at least that's what i think

SebSter

10-16-2005, 01:59 PM

To quote Albert Einstein:

“317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.”

its not undeniable fact, it's a fact a few ppl decided that thats whats gonna be. just like how some ppl decided the earth/humans came to be 2000 years ago. numbers are decided representations of what "we" perceive as a means to communicate. lets take for example this character here in the quotations "3", what if i decided that that character is the representation of a cow and i asked my fellow villagers if this was a good idea, eventually everyone accepted that that symbol would be a cow, take a wild guess what they would do if u said u would give them a 3 for free?!?

You're missing the point. This has nothing to do with the symbols we decided to represent numbers. This has to do with mathematics as a concept, not the written symbols on a piece of paper. Nobody decided that 0.999~ = 1.

Saying someone decided 0.999~ = 1, is like me saying someone decided that gravity will pull us towards the center of the earth.

Im sorry and I dont mean to be arrogant, but you are all wrong. Its not a matter of personal pride, Im not the one who decides it to be true. Its just how it is.

And if you can't follow the simple formula:

1/3 = 0.333~

1/3 * 3 = 0.333~ * 3

3/3 = 0.999~

.: 1 = 0.999~

then there is no hope for you...(and that is just the most basic way of showing it, there are more complicated proofs involving limits/functions, that there is just no reason to get into)

SebSter

10-16-2005, 02:05 PM

meh fundamentally flawed. 0.99999999~ isn't 1. but technically, 1/3 isn't 0.333~ if we talk in terms of rational numbers, even if we go to 100 digits past zero, 10 can't get split up into 3 evenly, aka to split up 10 into 3 different sums you'd have 3+3+4=10. so 1/3+2/3's DOES equal 1, but 1/3=/= 0.333~

:D

at least that's what i think

It's wrong. 1/3 = 0.333~. And it IS a rational number.

SebSter

10-16-2005, 02:10 PM

http://en.wikipedia.org/wiki/Decimal

Indeed, consider rational numbers which can be written as p/(2a5b) (i.e. the only prime factors in denominator are 2 and 5). In this case there is a terminating decimal representation. For instance 1/1=1, −1/2=−0.5, 3/5=0.6, 3/25=0.12 and 1306/1250=1.0448. Such numbers are the only real numbers which don't have a unique decimal representation, as they can also be written as a representation that has a recurring 9, for instance 1=0.99999…, −1/2=−0.499999…, etc.

There. Its done.

SebSter

10-16-2005, 02:11 PM

http://www.everything2.com/?node_id=14711

It is a little known, yet very important fact that the Arab numeral system, which is universally used nowadays, is not unambiguous. Any finite decimal fraction can be represented by an infinite decimal fraction by decrementing the last digit and adding a trail of 9's. Thus, the number 0.9999... is the same number as the number 1. This also holds for numbers like 0.4, which can be represented by 0.39999999...

SebSter

10-16-2005, 02:14 PM

http://mathforum.org/library/drmath/view/55746.html

There's no doubt that this equality is one of the weirder things in

mathematics, and it _is_ intuitive to think: No matter how many 9's

you add, you'll never get all the way to 1.

But that's how it seems if you think about moving _toward_ 1. What if

you think about moving _away_ from 1?

That is, if you start at 1, and try to move away from 1 and toward

0.99999..., how far do you have to go to get to 0.99999... ? Any step

you try to take will be too far, so you can't really move at all -

which means that to move from 1 to 0.99999..., you have to stay at 1.

Which means they must be the same thing!

moregothanshow

10-17-2005, 09:33 AM

so it's true, a higher being said there will be light and there was light! then he said some other stuff and now we are essentially brothers and sisters from the same 2 parents! this is exciting news!!

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