.9999...=1

[SUroot]

Its not a known number because you implied the 0s repeated for infinity and then ended in 1. An infinite number doesn't end.


But this whole conversation is about how .999...=1

1-0.999...=x
1-1=x
X=0

No because you assume in this that 0.9999... = 1 which it doesn't. If 0.9999... = 1 and the problem is set out to either prove or disprove that, you cannot make the assumption within the problem. It must be the outcome.

Its like using the word you are defining in definition.


Even though Wikipedia says .9999... is 1, its not

 

[Rxpert83]

I'm saying you cant get the number you presented from the equation given

I digress, we wont keep running circles with the same points. Someone else can chime in.

Have a good one.

 

[dan330]

SUroot,

the issue is.. you expressed an infinite reoccurring "0".. but tried to add and end to it with a "1".

the issue is.. how can it be? infinite means to go on FOREVER.. there should be no end. once you put and end to it.. then it is not infinite. see the problem?

 

[SUroot]

Yes dan330. I "get" the problem. You're saying I can't have an infinite number and round up by a 1 at "the point at infinity", even though we did that to get 0.999.... to become 1

 

[SUroot]

Ok I'm going to give up now. Mathematically it is unprovable that .999... does not equal 1, even though it doesn't, logic tells us that but for those whom subscribe to maths' truth, logic is a feutile argument. Even using hyperreals, Riemann spheres and limiting cases it can always be refuted. It's unprovable both ways because its an infinite loop of refuting arguments where nothing is agreed except that 0.999... = 1 is a mathematical fact.

So y'all stick with maths and i'll stick with logic

 

[big_z]

Ok I'm going to give up now. Mathematically it is unprovable that .999... does not equal 1,

.999... is a geometric series. Geometric series with the properties that .999... has converge to a finite number, and that number is easily calculated. This is provable, and is taught in all second semester calculus classes. Your belief is as mathematically incorrect as believing that

1 + (1/2) + (1/4) + (1/8) + (1/16) +...

does not equal 2, or that

.1111111...

does not equal 1/9.

 

[SUroot]

So as much as you argued 0.999... = 1, you're now saying you can prove the opposite, unrefutably? Go for it. Or did you misread what you quoted? If you didn't misread and you are countering the fact that it is unprovable without refute, you quoted out of context and missed the important part out.

 

[big_z]

I screwed up the quote. Sue me.

 

[SUroot]

What's the address of your lawyer?

But seriously, if you have a mathematical example that goes a long way towards disproving 0.999... = 1, even if it's not unrefutable, I'd be interested to see it.

 

[Mikestony]

I just want 1 cookie

 

[dan330]

are you keeping the .00001 of that cookie?? selfish!!!!!

 

[jhawkkw]

This thread is back from the grave?

 

[rabidhunter]

I would imagine if you're working in very specific conditions where a micrometer makes a difference, absolutley not. But for the rest of the world, yes.

 

[jhawkkw]

 

[Lordvincent 90]

 

[pbf98]

if you ask a computer you will get the answer of no.

bool isValid = false;
if(1 == .999)
{
isValid = true;
}
else
{}

isValid would stay false through that statement. If you're saying .999 = 1 you would have to say that 999 = 1000. Really it depends on what you're dealing with, if you have 999 in your checking account and you write a check for 1000 you're going to have a problem.

 

[jhawkkw]

if you ask a computer you will get the answer of no.

bool isValid = false;
if(1 == .999)
{
isValid = true;
}
else
{}

isValid would stay false through that statement. If you're saying .999 = 1 you would have to say that 999 = 1000. Really it depends on what you're dealing with, if you have 999 in your checking account and you write a check for 1000 you're going to have a problem.

A computer doesn't have a way to store an infinite number of terms, and any terminating number of 9's will never be equal to one. The idea is that if the number has an infinite amount of 9's, then it's exactly equal to one.

 

[Frisco]

Its not so much that your maths is wrong as it is that maths is wrong in general.

This ^

If math ("maths" to you brits ) were perfect everything would be perfect including the human brain that invented math.

To me, math is a handy myth. Handy in helping us to build things and go places, etc. Myth in that we can't rely on a system that self-negates, such as Pi, etc.

 

[pbf98]

It may not have any way of storing the infinite numbers, but the logic would still be the same.

To me .999... does not equal 1, because 0.999... is not 1.000... the only way it is, is when you round, which then you are just changing the number.

When I go shopping I do round everything to the nearest .50/.00 to make it easier to calculate my spending. Just because I say its that number, doesn't actually make it that number. The fact of the matter is it stays unchanged just as .999 does.

My opinion

 

[dan330]

It may not have any way of storing the infinite numbers, but the logic would still be the same.

To me .999... does not equal 1, because 0.999... is not 1.000... the only way it is, is when you round, which then you are just changing the number.

When I go shopping I do round everything to the nearest .50/.00 to make it easier to calculate my spending. Just because I say its that number, doesn't actually make it that number. The fact of the matter is it stays unchanged just as .999 does.

My opinion

i think you are not on the same page as the OP question.

you are right... {.999} is not equal to 1.0
but we are discussing {.999...} (the "9" is repeated to infinity)
the infinity part is what makes the difference ..

 

[sfbloodbrother]

i think you are not on the same page as the OP question.

you are right... {.999} is not equal to 1.0
but we are discussing {.999...} (the "9" is repeated to infinity)
the infinity part is what makes the difference ..

Right, its going on forever, we say it equals 1 but in reality it doesn't. Think of pi, we say it equals 3.14 and that's basically it, but it does not equal 3.14, as the number goes on forever.

 

[jhawkkw]

Right, its going on forever, we say it equals 1 but in reality it doesn't. Think of pi, we say it equals 3.14 and that's basically it, but it does not equal 3.14, as the number goes on forever.

3.14 is an approximation for pi, just like 22/7 is an approximation for it. 1 is not an approximation of .999..... repeated for ever because it can be proven that they are equal. There are several proofs, 4 to be exact, in earlier posts in this thread showing that.

 

[sfbloodbrother]

3.14 is an approximation for pi, just like 22/7 is an approximation for it. 1 is not an approximation of .999..... repeated for ever because it can be proven that they are equal. There are several proofs, 4 to be exact, in earlier posts in this thread showing that.

Its kind of odd to think that .999 = does in fact = 1. for me at least.

 

[jhawkkw]

Its kind of odd to think that .999 = does in fact = 1. for me at least.

Yeah, it's one of the oddities that show up in mathematics. There are other cases where two "different" looking things actually turn out to be the same. Graph/Group/Ring isomorphisms is an entire topic dedicated to where 2 different things that contain totally different elements can be proved to be the same because they a 1-1 mapping of their relationships.

 

[sfbloodbrother]

Yeah, it's one of the oddities that show up in mathematics. There are other cases where two "different" looking things actually turn out to be the same. Graph/Group/Ring isomorphisms is an entire topic dedicated to where 2 different things that contain totally different elements can be proved to be the same because they a 1-1 mapping of their relationships.

I may be taking that sometime in college, I want to be a computer engineer, and that requires a lot of math, so... I have a lot of math classes to look forward to.