Do you think 0.999999~ eqauls 1?

[Two|Bit]

This is bugging me because I saw a while back it being shown that it does eqaul 1. Does anyone know what I'm talking about... it was shown on G4tv. What are you opinions...

[hobey19]

http://en.wikipedia.org/wiki/Proof_t...99..._equals_1

(http://www.google.com/search?q=.999+...e=utf8&oe=utf8)

craig

[786ARS]

it does, 0.999999(recurring) * 10 = 9.999999999(recurring) - 0.99999999(recurring) = 9

9/9 = 1

[HAL9000]

Which leads me to my favorite proof.... I know what I know, and I know what I don't know, therefore, I know everything.

[David M]

It can in calculus....if you carry out the number infinitly. It becomes equal to one.

[786ARS]

my maths teacher showed my how to make 2=1, but i cant remembere how though, lol

[triviumrocks89]

no it doesnt 1 equeals 1 and 0.99999 equeals 0.99999
rounding it off just doesnt cut it for me. i hate it when i buy a hard drive thats supposed to be 200GB and its 181GB or when i thought i had 3Ghz but it just turned out to be 2.8Ghz. (this system was a gift)

[786ARS]

Originally Posted by triviumrocks89 no it doesnt 1 equeals 1 and 0.99999 equeals 0.99999 rounding it off just doesnt cut it for me. i hate it when i buy a hard drive thats supposed to be 200GB and its 181GB or when i thought i had 3Ghz but it just turned out to be 2.8Ghz. (this system was a gift)

with computers 200Gb by a manufacturer means 200 billion bytes, in reality it is 200*1024^3 bytes

the mathematics work, just try it out (see my earlier post)

[doctorgonzo]

The difference in hard drive capacity is due to using decimal versus binary counting.

Everybody knows that 1 KB of RAM isn't 1,000 bytes, it is 1,024 bytes. Computers are binary, so it makes sense to count things in terms of powers of two, and since 2^10 is about equal to 10^3, computer scientists started using "kilo" to mean 1,024 of something. Similarly, 1 MB of RAM isn't 1,000,000 bytes, but 1,048,576 bytes. 1 GB of RAM isn't 1,000,000,000 bytes, but 1,073,741,824 bytes.

That works all well and good for RAM, but for some reason hard drive manufacturers decided that 1 MB of hard drive space equals 1,000,000 bytes. However, Windows reports hard drive space using the binary notation.

So when a hard drive has a capacity of 200 GB, the hard drive manufacturers mean that it is 200,000,000,000 bytes. Dividing that by 1,073,741,824 bytes gives 186 GB as reported by Windows.

Some people think that to remedy the confusion, 1 KB should mean 1,000, and 1 KiB (notice the little "i" in there) should mean 1,024, and so on for other prefixes. This hasn't caught on, though.

Originally Posted by triviumrocks89 no it doesnt 1 equeals 1 and 0.99999 equeals 0.99999

That's true, but we're not talking about whether 1 = 0.99999. 0.99999 certainly doesn't equal one, but 0.9 followed by an infinite number of nines does.

[David M]

Originally Posted by triviumrocks89 no it doesnt 1 equeals 1 and 0.99999 equeals 0.99999 rounding it off just doesnt cut it for me. i hate it when i buy a hard drive thats supposed to be 200GB and its 181GB or when i thought i had 3Ghz but it just turned out to be 2.8Ghz. (this system was a gift)

If you ever take calculus and you get .9999999 as an answer, if you write down 1 as an answer on the test, I can guarantee you that you will not fail the test.

It has to do with a number approaching a limit. You can never get there but at the limit the number is a whole number and that whole number IS the answer. Not a repeating decimal. This is how the orbits of the planets were first calculated. To this day Newtons equations using calculus are still used and they are accurate. The bottom line is the correct answer right? The equations do not get you exactly there, but they get you so damn close that it becomes very obvious what is the correct answer.

Computer manufacturers have to round off numbers just for simplicities sake. It's unrealistic to expect them to give a number out to 12 decimal places.

[piasabird]

Yes it equals 1. Every .9 repeating gets closer and closer to 1 till it gets out to say the 100th iteration where it is so close to 1 that is actually is the same as one eventually. If you can see to infinity it is in essence equal to one.

[doctorgonzo]

Originally Posted by 786ARS my maths teacher showed my how to make 2=1, but i cant remembere how though, lol

Actually, it's (superficially) quite easy:

Define x=1
If x=1, then x²=1
Thus, x²-1=x-1
Factoring x²-1, you get (x+1)(x-1)
Thus, (x+1)(x-1)=(x-1)
Divide both sides of the equation by (x-1), and you get...
(x+1)=1
Since x=1, that means (1+1)=1, or 2=1.

This is invalid. Why?

[peekaboo]

are you guys kidding?
0.9999 equals 0.9999 and nothing else.
0.999_ (repeating) equals 0.999_ (repeating) and nothing else.

these values may be considered to be equal to 1 for practical purposes if they meet your accuracy requirements.

the correct definition should be "close enough to 1 for practical purposes/applications".

0.99 cups of sugar in a cake might be as good as 1 cup of sugar but 0.01 mm distortion in the focus of a sattelite lens might render it uselsess.

[doctorgonzo]

Originally Posted by peekaboo are you guys kidding? 0.9999 equals 0.9999 and nothing else. 0.999_ (repeating) equals 0.999_ (repeating) and nothing else. these values may be considered to be equal to 1 for practical purposes if they meet your accuracy requirements.

That's incorrect. 0.99999... repeating to infinity equals 1. It does. That's been mathematically proven in countless ways. To say otherwise is to say that mathematics is in error.

Remember, we are not talking about 0.999999, nor 0.999999999999999999999999999999, nor 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999. None of those are equal to 1, that is certainly true. But if those nines go on not to a hundred, not to a billion, not to a googol, not to a googol^googol, but to infinity, then it is equal to one. Not "close enough", but completely, unambiguously equal.

[Eriol]

Originally Posted by doctorgonzo Actually, it's (superficially) quite easy: Define x=1 If x=1, then x²=1 Thus, x²-1=x-1 Factoring x²-1, you get (x+1)(x-1) Thus, (x+1)(x-1)=(x-1) Divide both sides of the equation by (x-1), and you get... (x+1)=1 Since x=1, that means (1+1)=1, or 2=1. This is invalid. Why?

Gonzo,
It's invalid because if x=1 and your dividing x-1 then really your trying to divide by zero, which we know doesnt work.

and gonzo is right, its exactly equal to one, not close but equal. Its really about the power of infinity.

[doctorgonzo]

You get a cookie!

[Eriol]

I like cookies =)

I got one
i=i
√-1 = √-1

√(1/-1) = √(-1/1)

√1/√-1 = √-1/√1

√1 x √1 = √-1 x √-1
1=i^2

1=-1

Where's the fallacy

[peekaboo]

have you guys ever studied those proofs?
do you know how they justify 0.99999_ equaling 1?
the same way (dx)^2 = 0, by assuming that it is small enough to practically (!!!) be zero.

do you really understand the logic behind infinity?
what is infinity?
is 0.9999_(repeating a billion times) not close enough to 1 but add a ridiculously small number to it (smaller than what is needed to make it exactly one) to make it 0.9999_(repeating a googleflex times) and it suddenly becomes 1?

[doctorgonzo]

Yes, I do understand the proofs, and I understand the logic behind infinity. And yes, 0.9 repeating is one. hobey posted a couple links showing some proofs, here is the first one I learned in algebra:

1/3=0.33333... repeating, correct?
So 1/3 + 1/3 + 1/3 = 0.99999 repeating, since 3+3+3=9 in every single decimal place, and there is no carrying to worry about.

But 1/3 + 1/3 + 1/3 = 1 by simple fractional addition.

So 1 = 0.9999.... repeating.

[Trent Steel]

... means repeating to infinity


let A=0.99999...
thus ten times A is 10A=9.99999...
subtract to get

10A=9.99999...
- A=0.99999...
_________________
9A=9.00000...

now solve for A

9A=9
9A/9=9/9
A=1

from before
A=0.99999...
thus 1=0.99999...

[Eriol]

Originally Posted by peekaboo do you really understand the logic behind infinity? what is infinity? is 0.9999_(repeating a billion times) not close enough to 1 but add a ridiculously small number to it (smaller than what is needed to make it exactly one) to make it 0.9999_(repeating a googleflex times) and it suddenly becomes 1?

you have to remember that .99999....reapeating a billion times or even a googleflex times is not the same thing as infinity

[Stuey]

Adhering to common scientific significant figure rules, 0.99999~ = 1.00. Nothing beyond the third decimal place counts.

[Eriol]

Originally Posted by Stuey83 Adhering to common scientific significant figure rules, 0.99999~ = 1.00. Nothing beyond the third decimal place counts.

Stuey,
that may be true, but different topic. Scientific significant digits is a way of estimating. 0.9999....... is not estimated to be 1 it is exactly equal to 1.

[peekaboo]

once again, 0.3333_ is an approximation of 1/3. it's pretty damn close but it's not 1/3.
just like 0.167 is an approximation of 1/6 (or perhaps 0.16666666666667).

so please don't tell me that 0.3333_ x 3 = 1
it equals 0.999999_ which is also pretty damn close to 1 but not exactly.

1.41 is approximately the square root of 2.
2.718 is almost e.
3.14 is close to Pi.

Stuey, if you're designing a road then you could treat 0.0X meters as insignificant but if you're designing a silicon wafer then you treat 0.00X... as very significant even if your design units are millimeters.

[Eriol]

[QUOTE=peekaboo]once again, 0.3333_ is an approximation of 1/3. it's pretty damn close but it's not 1/3.
just like 0.167 is an approximation of 1/6 (or perhaps 0.16666666666667).

so please don't tell me that 0.3333_ x 3 = 1
it equals 0.999999_ which is also pretty damn close to 1 but not exactly.

QUOTE]

but .99999.. does equal one not close but equal.
did you see trent's proof above.

and 1/3 does equal .33333....(to infinity)

so another way of showing .999.... =1 is
1/3 = .33333....
2/3 = .66666....
3/3 = .99999....
1 = .99999....

[HAL9000]

Originally Posted by peekaboo once again, 0.3333_ is an approximation of 1/3. it's pretty damn close but it's not 1/3. just like 0.167 is an approximation of 1/6 (or perhaps 0.16666666666667). so please don't tell me that 0.3333_ x 3 = 1 it equals 0.999999_ which is also pretty damn close to 1 but not exactly.

BUT, using legitimate proof, 0.9999999... is proven to be 1, so what you need is a proof that prove it is NOT 1... same applies for the 0.333...x3=1

[786ARS]

this rule that recurring decimals however cant be applied to simple mathematics, when defining an inequaliy.

eg: 1 signs pointless because the value is equal to the maximum value, when it is supposed to be smaller than it.

[Stuey]

Originally Posted by peekaboo Stuey, if you're designing a road then you could treat 0.0X meters as insignificant but if you're designing a silicon wafer then you treat 0.00X... as very significant even if your design units are millimeters.

Yes, but even if you design a wafer to certain parameters, you're going to get certain variance in the end product. If you produce 10 wafers of CPUs, your CPUs are not going to perform at the same clock speeds. Mathematical accuracy and realistic accuracy are never going to match up with each other.

Anyways, theoretically, 0.999999~ is NOT equal to 1.00, EVER. Realistically, 0.999999~ is equal to 1.00. Both answeres (yes it's equal to one, and no it's not equal to one) are valid, depending on the perspective.

[David M]

0.999999 ad nauseum is a repeating decimal which is going out to infinity which by definition means that it is equal to 1. It is not equal to 0.99999 because the last digit never ends...it extends to infinity. To say it is equal to 0.9999 is to say it ends...which it does not end. It goes on forever.

Mathematically, it is the number 1. It's not even debatable. Ask any mathematician.

This is simply another way of describing the number one. Many equivalent things in mathematics can be described differently but in the end, you are describing the same thing. You have to remember, math is a way of describing things which can be quantified. One unit of anything can be descibed in many different ways using mathematics....NOT solely by describing one unit of something with the number "1". 0.99999..out to infinty is another way of describing the number one without actually using the description of "1"

Can a vehicle be called an automobile and a car?..can both be an accurate description? Yes. Can one unit of something be described be described as "1" and can it be described as 0.99999 out to infinity?...yes. Both are accurate descriptions of a concept called "one"

Its easy to forget that numbers do not exist unto themselves, they are concepts assigned to something in the physical or abstract world. A description is not a "thing". There are equivalent things in this world and equivalent descriptions. Don't confuse the two. Some here are trying to say that equivalent descriptions are not the same thing...which is not true.

Infinity is a difficult concept just like black holes and time not being linear. But it exists.

[Eriol]

very well put david