Do you believe that 1= .999~

[Tobbzn]

If we call 0.999~ for X, then
9.999~ = 10X. If so, then
10X-X = 9X, thus
9.999~-0.999~ = 9.
If 9X = 9, then X = 1. We agreed that we called 0.999~ for X, thus
0.999 = 1.

Also;
1/3=0.333~
0.333~x3 = 0.999~
And thus 1 = 0.999~

More about this found on http://en.wikipedia.org/wiki/0.999...

Now, this is a coincidence created by the way our numerical system works, and would not be the case with certain other numerical systems.
Do you believe?

[Note; There is a thread about this, but it was made in March and is now closed.]

EDIT: Thanks to Samuraid for the idea of adding a wikipedia links.

 

[Mechanical Man]

Maybe it can be proved with infinitesimal calculus, but I never tried.

 

[Hakeem]

If you can comprehend infinite decimals, then maybe you can say no.

 

[Tobbzn]

If you can comprehend infinite decimals, then maybe you can say no.

Can you? I were of the opinion that it was if you had no definition of infinite numbers, you wouldn't understand it, because then you'd round it off at the end, and 1 would equal to 1. Triple of 0.333~ will always be 0.999~, but since it's a 9, calculators and basic math tells you to round it off upwards.

That's the problem with infinite numbers.

 

[Hakeem]

Can you?

I don't think anybody can.

 

[donut3.5]

The minute you can write out infinite 3's, 9's, or any other number, I'll believe that 1=.999.
--donut3.5--

 

[PurplePoot]

I'd agree, but because it becomes silly if you don't round after a certain point...

 

[Wolverabid]

1 is a whole number; 0.999 (or any decimal or fraction) is not.

 

[PurplePoot]

Wolverabid, the important fact is that it continues forever, so the question of rounding comes up.

Also, the glitch with the aforementioned formula stands.

 

[Samuraid]

Every proof you need:
http://en.wikipedia.org/wiki/0.999...

 

[donut3.5]

Wolverabid, the important fact is that it continues forever, so the question of rounding comes up.

Meh, rounding .59 to the tenths place to become .6 doesn't mean that .59=.6
I don't see why, even when dealing with infinite place, the rounding would make them equal.
--donut3.5--

 

[PurplePoot]

Because it's really really silly to calculate something to infinite digits =/

Anyhow, even if not, anything with a repeating infinite number of digits has the flaw pointed out in the original post.

 

[Infinitynexus]

Pretty much the dumbest question ever asked.. As if I believe that 3 times a fraction = almost one.

 

[SimonKurciski]

Do you believe

I'm not informed in this matter, and I don't have an opinion. But it bothers me somewhat that you ask if we "believe". It's not a matter of belief. It's a matter of evidence and calculation. Math is not mystical.

 

[Cheeder]

Wolverabid, the important fact is that it continues forever, so the question of rounding comes up.

Also, the glitch with the aforementioned formula stands.

WHY does the "issue" of rounding come up? That doesn't make any sense.

EDIT:

Tha fallacy with the OP is that you can multiply infinity... You can't.

 

[Ljusdahl]

I'm pretty sure 1=1

 

[HINDYhat]

0.99999 to infinite digits can be represented with limits, I think.

But that doesn't make it equal to 1. There is still an infinitissimal value added to it. Of course, when you have infinite digits, you can substitue that value with 1, because the difference is tiny. Other than that, saying things like:
0.59 = 0.6
is completely ridiculous -.-

Equivalence should only be noted when 0.999 has infinite 9 digits.

 

[Dr00d]

I come to the internet for THIS IS SPARTA pics and pr0n, not math. -.-'

Hence forth you need a "I don't care" poll option.

 

[Mechanical Man]

Hindyhat: That people have just forgot to write ~ at the end, which the author of the thread showed as a limitless amount of '9' digits

Dr00d: Some people like THIS IS SPARTA pics and pr0n, some math. The good side of internet is that it can satisfy both types of people

 

[The_wand_mirror]

1 = 1

Djeez even humans don't understand they're own inventions -,-

 

[HINDYhat]

Well, isn't this how differentiation works?

f'(x) = (f(x+h)-f(x))/h

Where h is the smallest number before 0.

So technically, if this weren't right, then differential calculus would be bogus.

 

[Razorbrain]

3 Words for you

Your math fails

0.999~ x 10 = 9.999~ with 90 at the end

now, 90 - 99 = -9

therefore, 9.0 - 0.000~ with a 9 at the end, becomes 8.999~ with 1 at the end

so that means our final calculation becomes 9x = 8.999~ with 1 at the end

which concludes, 0.999~ is not equal to 1

 

[Cheeder]

Well, isn't this how differentiation works?

f'(x) = (f(x+h)-f(x))/h

Where h is the smallest number before 0.

So technically, if this weren't right, then differential calculus would be bogus.

A correction in terminology - Smallest DIFFERENCE before 0.

Infinity is not a number, and therefore 0.999~ can never even REACH one.
However, infinity is represented by a circle, or figure eight, each an enclosure, representing one whole, or no difference; cyclic.

One minus infinity = 0.999~
but
Infinity plus one could be anything, any number, as it does not stop. Infinity never started but hey.. hahaha "plus one" is like saying "plus 'X'", they are both the same.



EDIT:

3 Words for you

Your math fails

0.999~ x 10 = 9.999~ with 90 at the end

now, 90 - 99 = -9

therefore, 9.0 = -0.0~ with 9 at the end

so that means our final calculation becomes 9x = 8.999~ with 1 at the end

which concludes, 0.999~ is not equal to 1

Your math fails, and math in general just sucks.

Infinity doesn't have an end so there cannot be a '0' at "the end".

You cannot multiply infinity, at least in numbers, with the same numbers.. You cannot have 10 infinitys of the same number, they would always cancel themselves out to one set. That's what i mean by same numbers, like the given example of 0.999~

As for 0.999~ times, or even divided by, 0.888~ (or any other number), you still have a decimal because you cannot compute what does not end for you to compute. You have to wait for infinity for it to end before you could finish a calculation.

I have no idea how you got to your conclusion, but it is correct.

Point (.) ANYTHING is just a fraction. Think of a pie chart. Now think of 1/2 of the pie. Then 1/3, 1/4, 1/5 and so on, infinitely. The pie slice, from half, gets smaller and smaller, forever, but does not quite ever reach a full pie, or whole amount.

 

[HINDYhat]

Heh, I don't know my terminology, I haven't really had differential/integral calculus classes yet...

But Razorbrain, care to explain how you worked that out?? You lost me at 9.0=-0.0~... because that's clearly untrue.

 

[Razorbrain]

woops, typo

too short message ftl

 

[SimonKurciski]

.99999999 to infinity IS equal to one.

http://en.wikipedia.org/wiki/0.999...

Samuraid already posted this link.

 

[Cheeder]

.99999999 to infinity IS equal to one.

http://en.wikipedia.org/wiki/0.999...

Samuraid already posted this link.

You can't get TO infinity. hahahaaaaahhhhhh.. hmm.

Do you believe everything you read, are told? Do you believe it like a fool because it's popular opinion?

Yes, infinity can be REPRESENTED as one (1) but it is not the same as one. And one is not the same as infinity, nor can one equal infinity.

0.999~ is a fraction of one and therefore cannot be equal to or the same as one. This is basic math.

 

[The_wand_mirror]

I dont get shit of this, i probably should stick to dutch -.-

 

[Kofi_Banan]

so if 1 - 0.000...01 = 1
then if i take a 0.000...01 part of cookie i got 0.9999...9 and 0.00000...001 cookie
which equals
to 1 and 0.0000...001 cookies
so if i will do that infinity times i will have infinity cookies from 1 cookie ?

 

[Hakeem]

I come to the internet for THIS IS SPARTA pics and pr0n, not math. -.-'

Hence forth you need a "I don't care" poll option.

Then don't vote. Do I really need to spell it out for you?

0.999~ x 10 = 9.999~ with 90 at the end

now, 90 - 99 = -9

therefore, 9.0 - 0.000~ with a 9 at the end, becomes 8.999~ with 1 at the end

so that means our final calculation becomes 9x = 8.999~ with 1 at the end

which concludes, 0.999~ is not equal to 1

No, see, it goes on forever. There is never a 0, 1, or 9 at the end. There is no end.
How can it go on forever you ask?
Well, give me any number, and I'll give you something greater, something less, and something with more digits.

math in general just sucks.

Your brain lacks the capacity to understand why math is awesome.

You cannot multiply infinity, at least in numbers, with the same numbers.. You cannot have 10 infinitys of the same number, they would always cancel themselves out to one set. That's what i mean by same numbers, like the given example of 0.999~

0.999... going on forever is not comparable to infinity.
Also, consider a line (infinity) has an infinite number of points.
Now, consider a plane (infinity * infinity) which also has an infinite amount of points.

Do you believe everything you read, are told? Do you believe it like a fool because it's popular opinion?

Did you notice that the poll clearly illustrates that popular opinion (in this forum anyway) is that this is not true? I bet you didn't, and furthermore, I bet you're right about popular opinion being wrong (in this forum anyway).

0.999~ is a fraction of one and therefore cannot be equal to or the same as one. This is basic math.

Basic? Is it basic because it involves understand infinity? (Also, 9/9 is a fraction.)

so if 1 - 0.000...01 = 1
then if i take a 0.000...01 part of cookie i got 0.9999...9 and 0.00000...001 cookie
which equals
to 1 and 0.0000...001 cookies
so if i will do that infinity times i will have infinity cookies from 1 cookie ?

In the last few decades, researchers of mathematics education have studied the reception of this equality among students. A great many question or reject the equality, at least initially. Many are swayed by textbooks, teachers and arithmetic reasoning as below to accept that the two are equal. However, they are often uneasy enough that they offer further justification. The students' reasoning for denying or affirming the equality is typically based on one of a few common erroneous intuitions about the real numbers; for example that each real number has a unique decimal expansion, that nonzero infinitesimal quantities should exist, or that the expansion of 0.999… eventually terminates.

To sum it up:

reasoning for denying the equality is based on erroneous intuitions, for example, that the expansion of 0.999… eventually terminates.

1/3 = 0.333... in base 10.
But in base 3, 1/3 = 0.1
0.1 multiplied by 3 (again in base 3) is equal to 1.
If you don't understand base numbers, then don't post.

 

[Razorbrain]

1/3 = 0.333... in base 10.
But in base 3, 1/3 = 0.1
0.1 multiplied by 3 (again in base 3) is equal to 1.
If you don't understand base numbers, then don't post.

now, i might now understand, since i dont calculate math in english, but

are you saying 0.3 x 3 is equal to 1?

anyway, there is a better way of making 10/3 = 3.33(not infinite amount of 3s, but maybe not just 2)

lets say, i have a birthday cake in vanilla(not hardened, like its been on the floor for 6 weeks)

now, if i divide the cake into 3 parts with a kitchen knife, parts of the cake will still remain on the knife. It doesnt matter what instrument i use, same thing will still happend. I know its a bad example, but combining math with physics is just funnier to do

 

[Captain Griffen]

Mathematically, they are equivilent for all practical purposes.

They are seperate entities, and not the same, however.

Consider:

0.999... = 1 - 1/infinity

If 0.999... = 1 then:

0 = 1/infinity

Therefore:

0 = any value

 

[Eleandor]

And where's your argumentation to say that 0 = any value?

 

[Hakeem]

now, i might now understand, since i dont calculate math in english, but

are you saying 0.3 x 3 is equal to 1?

No.

anyway, there is a better way of making 10/3 = 3.33(not infinite amount of 3s, but maybe not just 2)

It DOES go on forever, do the long division, you always have a remainder of 1 that must be divided.

lets say, i have a birthday cake in vanilla(not hardened, like its been on the floor for 6 weeks)

now, if i divide the cake into 3 parts with a kitchen knife, parts of the cake will still remain on the knife. It doesnt matter what instrument i use, same thing will still happend. I know its a bad example, but combining math with physics is just funnier to do

So you are using an imperfect tool to divide?

 

[Razorbrain]

Okay, i just read a big bit of the wiki page Hakeem

You are saying, that 1 / 3 = 0.333~

and 0.333~ x 3 is equal to 0.999~

so, therefore, 1 = 0.999~

am i correct?

and frankly, those "wikipedia geniuses" might know alot, but they sure have their flaws. They have said, that in an algebraic way, this is possible

they say, that (0 / 0) x 1 = (0 / 0) x 2 which leads to 1 = 2 (since i can remove the (0 / 0) on both sides)

now, they dont seem to know that 0 / 0 = 1 since A / A = 1 and if A = 0, then 0 / 0 = 1 must be true, correct?

and 1 x 1 cannot be the same as 1 x 2

 

[Kofi_Banan]

You cant division anything by 0 , isnt that one of math laws??

there can be 0/1 but not 1/0 go to school!

 

[Razorbrain]

TELL IT TO THEM!

 

[Samuraid]

TELL IT TO THEM!

0/0 is not zero, nor infinity, nor any defined value. It is called an indeterminate form and it is inherently undefined. While some other forms can be reduced to an evaluable limit using a technique such as l'Hospital's rule, 0/0 itself cannot.

So

(0 / 0) x 1 = (0 / 0) x 2

is not a valid equality.
One undefined expression != another undefined expression.

 

[Cheeder]

Mathematically, they are equivilent for all practical purposes.

This i have come to agree with. I gave an example of 0.999~ being practical, and i still had one molecule!

If you take WILLTHEALMIGHTY's avatar, and image the very center being a molecule. Now imagine it getting smaller and smaller, everything around it seems to be getting bigger and bigger. But no matter how small it gets, in comparison to our relationship to the molecule as obervers, meaning we are moving with it, it's still the same. Not only is it the same but it won't ever go away. It's just there; ONE molecule.
Of course it's getting smaller and smaller, but with a practical use for the math, and math is ONLY practical because we apply it to matter, it CAN be ACCEPTED as the same as one.

Used in math for the sake of math it cannot be acepted as one (1). Used for a practical purpose of relating it to matter, or even the idea of a material situation, it can be accepted as one (1).

On the flip-side, my example of an infintely shrinking molecule does not incorporate the idea of a given one (1) to compare an infinitely shrinking molecule to. Meaning, i give no mention of a base for the original mass of a molecule AS one (1).

So... damn. I mean, i think if you compared an infinitely shinking molecule to a base mass of an original molecule, it still isn't practical to be used as one in a mathematical situation - because the mass of the fractioned molecule is still obviously smaller than the base mass.

I used a practical situation where the infinity IS one because it exists as something, but compared to a base mass it cannot be equal to it.

My opinion, and my conclusion is that it can be CONSIDERED one (1) in a practical situation. The philosophy then becomes finding a practical situation.

EDIT:

A way of EXPLAINING 0/0 in a practical sense to convey the message of how impossible it is is by substituting the zeros with either the idea of "nothingness" or "infinity".