2/2 is a sum; it literally means 2 divided by 2. It is more than one number.Rough Sausage said:
What I am saying is that there is no way of writing the same (single) number in two different ways.
Poll: Does 0.999.. equal 1 ?
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What I am saying is that there is no way of writing the same (single) number in two different ways.
Yes, there is a very short mathematical proof already mentioned on this thread, but I will repeat it:
x is used to represent 0.9999999.....
Therefore x=0.9999999.....
10x= 0.9999999.....*10 = 9.9999999.....
9x = 10x - 1 = 9.9999999..... - 0.9999999..... = 9
9x = 9 Therefore x = 1
0.9999999..... = 1
x is used to represent 0.9999999.....
Therefore x=0.9999999.....
10x= 0.9999999.....*10 = 9.9999999.....
9x = 10x - 1 = 9.9999999..... - 0.9999999..... = 9
9x = 9 Therefore x = 1
0.9999999..... = 1
This is getting tiresome, this isn't a matter of opinion any more than putting that 1 + 1 = 2 up to a vote is.
As a computer scientist, I can tell you that what you're seeing is a floating point rounding error. In general mathematics, they are equal, but (being infinitely long) the series is impossible to represent in digital form.PxDn Ninja said:
Please, preach your soothing wisdom further.Spencer Petersen said:
2/2 is an expression, not a sum. Summing is specifically the act of adding numbers together. Expressions are similar to equations, but they are missing one key element of equations: They do not have an equals sign in them. 2/2 is an expression, 2/2 = 1/1 is an equation, and neither are sums.Puzzlenaut said:
He is saying that if they where two seperate numbers, you could easily find another number between them. For instance, 0.2 and 0.3 are seperate numbers, and you can fit fractions like 0.27 or 0.296 in between them. But if the number 0.999... is recurring forever, you cannot possibly find a number that is less than 1.0 but greater than 0.999... If you can not find a fraction small enough to fit between the two, one must not be greater than the other. They must therefore be equal.Tetranitrophenol said:
yes.
every time you add a 9 digit to the end, it gets a closer towards 1.
it 'tends' towards 1
this means in 'infinity' or, when there are infinite 9 digit, it equals one.
for all practical purposes.
note the proofs that say
1/3 = 0.333...
2/3 = 0.666...
so 3/3 = 1 = 0.999...
are pointless...
who the hell says 1/3 = 0.333...
that's no more unquestionable as saying 1 = 0.999...
or think of it this way:
1= 0.9 + 0.1
= 0.99 + 0.01
= 0.999 + 0.001
= 0.9999 + 0.0001
= 0.999... + 0.000...
yes, thats right, there is no '1' after the infinite number of 0 digits.
the (infinite + 1)th digit is not 1.
there is no infinity + 1, infinity + 1 is infinity, and we already said the infinite digit is 0!
...
infinity + any number or 0 is infinity
infinity + infinity is infinity
infinity - infinity is 0
any number except 0, divided by 0, is infinity
infinity divided by infinity is 1
infinity multiplied by any number is infinity
and probably, any number divided by infinity is 0
note that there is negative infinity, and signs work the same way they do with any other number, when doing operations with infinity.
-infinity / infinity = -1 ect...
again, practically speaking...
every time you add a 9 digit to the end, it gets a closer towards 1.
it 'tends' towards 1
this means in 'infinity' or, when there are infinite 9 digit, it equals one.
for all practical purposes.
note the proofs that say
1/3 = 0.333...
2/3 = 0.666...
so 3/3 = 1 = 0.999...
are pointless...
who the hell says 1/3 = 0.333...
that's no more unquestionable as saying 1 = 0.999...
or think of it this way:
1= 0.9 + 0.1
= 0.99 + 0.01
= 0.999 + 0.001
= 0.9999 + 0.0001
= 0.999... + 0.000...
yes, thats right, there is no '1' after the infinite number of 0 digits.
the (infinite + 1)th digit is not 1.
there is no infinity + 1, infinity + 1 is infinity, and we already said the infinite digit is 0!
...
infinity + any number or 0 is infinity
infinity + infinity is infinity
infinity - infinity is 0
any number except 0, divided by 0, is infinity
infinity divided by infinity is 1
infinity multiplied by any number is infinity
and probably, any number divided by infinity is 0
note that there is negative infinity, and signs work the same way they do with any other number, when doing operations with infinity.
-infinity / infinity = -1 ect...
again, practically speaking...
Technically yes, but in most situations I'd go with with no.
Here's a hypothetical, an omnipotent figure pops up in front of you and makes you an offer, you can either be extremely rich your entire life, and have a 99.999...% chance of dying, or to make it even worse some sort of death free unthinkable hell, after you take that option. Or you could just walk away, and not die. Basically a 100% chance, of not dying. I would go with option B, because anything is statistically possible unless there is an absolute 100% chance of it not happening, which even then it is arguable that nothing is absolute.
Here's a hypothetical, an omnipotent figure pops up in front of you and makes you an offer, you can either be extremely rich your entire life, and have a 99.999...% chance of dying, or to make it even worse some sort of death free unthinkable hell, after you take that option. Or you could just walk away, and not die. Basically a 100% chance, of not dying. I would go with option B, because anything is statistically possible unless there is an absolute 100% chance of it not happening, which even then it is arguable that nothing is absolute.
The flaw with this is that you have one less than infinity 9s after the decimal in 9.999 so it would not be 9 but 8.999...1Spencer Petersen said:
OT they are not equal. The reason they always appear to be is that the difference is so negligible that it can be ignored. You could say .999... ≈ 1 but that is because it is approximation. Also 1/3 does not equal .333... it is just a common approximation like pi ≈ 3.14
christ, can we drop this already? 0.99999999999999999999 is NOT 1 if it were 1, THEY WOULD JUST CALL IT 1!
it's just a teeny tiny bit smaller than one, but it is not one, no matter how many times you do your fancy algebra.
and (9.9999999999-0.99999999999) is NOT 9, it is 8.99999999991
using rounding errors does not make you smart.
it's just a teeny tiny bit smaller than one, but it is not one, no matter how many times you do your fancy algebra.
and (9.9999999999-0.99999999999) is NOT 9, it is 8.99999999991
using rounding errors does not make you smart.
No, it doesn't.Zukhramm said:
When you see this in a math problem, you must substitute 0.999... for 1 because there is no way to use an infinite number in a math problem. However, as soon as you substitute 0.999... the problem becomes an approximation, because 1 does not equal 0.999 repeating. Look at my post earlier to see what I mean.
For me, this thread is not about the mathematics anymore. 0.(9) = 1, you can follow the links previous posters have posted for proofs. There is no room for opinion or 'personal beliefs'.
How do people get the arrogance to answer a resolute 'no', while trained mathematicians have come to the conclusion the answer is 'yes'? I would really like to know what credentials these nay-sayers have.
Sure, the statement 0.(9)=1 might be counterintuitive to some, and I can imagine an appeal to authority is hardly convincing, but rather than coming to the conclusion that 'experts are wrong, I am right', can't one admit one's ignorance and realize that more likely the experts are right and that one lacks the mathematical insight or knowledge required to fully comprehend the proof? Or do we really think that those gifted mathematicians are bigoted when it comes to this issue, or that they are lying to keep the public ignorant and that we, great independent thinkers, should think for ourselves and, despite our lack of expertise, reject their 'ideas'?
Being critical and skeptical, I find, is a good thing. But it's also important to recognize your own ignorance and admit that others are more likely to know better.
I'm sorry if my formulation was somewhat chaotic, or my tone aggressive and condescending, but things like these tend get me a bit annoyed
How do people get the arrogance to answer a resolute 'no', while trained mathematicians have come to the conclusion the answer is 'yes'? I would really like to know what credentials these nay-sayers have.
Sure, the statement 0.(9)=1 might be counterintuitive to some, and I can imagine an appeal to authority is hardly convincing, but rather than coming to the conclusion that 'experts are wrong, I am right', can't one admit one's ignorance and realize that more likely the experts are right and that one lacks the mathematical insight or knowledge required to fully comprehend the proof? Or do we really think that those gifted mathematicians are bigoted when it comes to this issue, or that they are lying to keep the public ignorant and that we, great independent thinkers, should think for ourselves and, despite our lack of expertise, reject their 'ideas'?
Being critical and skeptical, I find, is a good thing. But it's also important to recognize your own ignorance and admit that others are more likely to know better.
I'm sorry if my formulation was somewhat chaotic, or my tone aggressive and condescending, but things like these tend get me a bit annoyed
I asked my friends this... and they didn't know what the fuck I was talking about. So thanks, for this thread. I think it's generally accepted that any number divided into itself equals 1.
1/3 = .333....
2/3 = .666....
3/3 = 1
The .9999... stretches on to infinity yes, but, from a logical perspective. One must look at it as 1. Otherwise we'd all go mad. Stop with these math problem threads! You're making me look like a moron.
1/3 = .333....
2/3 = .666....
3/3 = 1
The .9999... stretches on to infinity yes, but, from a logical perspective. One must look at it as 1. Otherwise we'd all go mad. Stop with these math problem threads! You're making me look like a moron.
In "reality" infinity might not exist, so 0.(9) would never actually occur... you might just get a number that has so many 9 after zero that you can't possibly count them all before the universe ends... and it would not be 0.(9)... you'd never be able to tell though.Zukhramm said:
And of course if it does exist there would never be a noticeable difference between it and 1 even if the universe lasted for infinity...
That's why it works even if math proof could be wrong, because there's no way it can affect reality differently then 1 does...
The proof is pretty simple, everyone with any math knowledge should understand it...karplas said:
The problem is that understanding it's real world justification is harder... way i see it is that because the 9 goes on for infinity it would take infinity for .(9) to be different from 1, and because infinity never ends it never is...
So yeah, magic...