0.999... = 1

[Relevance]

I can use infinite series to "prove" that 0=1, or that 9999999999 = 0. Fool's proofs are very common and not so surprising.

... this is not a Fool's proof. There are no mathematical axioms violated.

tl;dr - .99999... does equal 1.

This is ridiculous...
0.999... Approaches 1 If and Only If
0.999... = 0.9 + 0.09 + 0.009 + 0.0009...
= a/(1-r)
=0.9/(1-0.1)
=0.9/0.9
=1
EDIT: Approaching symbols should have been used in that proof (-->) as opposed to (=) signs...

Maybe I'm missing the point. Are you trying to prove or disprove the claim?

 

[Snow Patrol]

I've seen something similar to this that tries to prove that 0 = 1 or something like that lol

 

[BEN007]

Second one is wrong...

You say 0.333... = 1/3.

But it doesn't:

1/3 is 0.3 with an infinite amount of 3s.
Whereas 0.333 can never be exactly one third; there always has to be a certain number of 3s.

I know it's not explained very well but oh well...

 

[Elfenones]

Bump.

 

[DeXoh]

The following image explains this concept well. It is no trick math; it is true.

http://i.imgur.com/BVtL9.png

I can use infinite series to "prove" that 0=1, or that 9999999999 = 0. Fool's proofs are very common and not so surprising.

Would you like to provide a so-called "fool's proof"? You can't prove 1 = 0 without committing a mathematical fallacy.

 

[Elfenones]

Bump, interested in re-opening this discussing to community.

 

[Imagine]

I've seen something similar to this that tries to prove that 0 = 1 or something like that lol

This is true though, 0 = 1 wasn't ^_^

Bump, interested in re-opening this discussing to community.

There really is no discussion to be had, .999... is clearly 1, you can't really argue the contrary.

 

[thatguy1234]

you can make x = any number. I think this is flawed. at the end of the day .9999999999999999 and 1 are different numbers. Anything will make sense if you think about it too much.

 

[MohtasaUnique]

http://sythe.org/showthread.php?t=1261769

Just throwing it out there. This has already been debated to fuck

 

[Proverbs]

a cat isnt a dog. thus .99999999999999999999999 cant be 1 (a whole different number)

 

[Faiden]

I've been thinking a lot about it since I'm studying advenced maths, but it'll always be a mistery

 

[Annex]

I've been thinking a lot about it since I'm studying advenced maths, but it'll always be a mistery

That's because this really isn't much of a math question as much as it is a flaw in our system of fractions. .9999999... only equals 1 because of our inability to properly represent the number. Proof of this actually exists because in the model of a black hole, the center of it returns as the fraction 1/0 which technically can never exist.

Mathematically .999999.. does equal 1 but that is ONLY because we have no truly accurate way to represent fractions that exist like that. Eventually we will learn how to properly represent these things and people will look at archives of this shit and laugh about how stupid people were.

 

[Imagine]

a cat isnt a dog. thus .99999999999999999999999 cant be 1 (a whole different number)

Have you read the thread?

Between any two numbers, there is always a number that is half way in between.

Now tell me a number halfway between .999... and 1.
That's right, there is none, because they are the same number.

 

[Proverbs]

Have you read the thread?

Between any two numbers, there is always a number that is half way in between.

Now tell me a number halfway between .999... and 1.
That's right, there is none, because they are the same number.

so if there is a 99.999999% chance of a successful launch, you're bascially saying its 100%?

 

[Imagine]

so if there is a 99.999999% chance of a successful launch, you're bascially saying its 100%?

99.999999 is not 99.999... repeating forever.

So no, I'm not saying it's 100%.

 

[malakadang]

Theoretically 0.999 recurring does = 1. However, to therefore say this is wrong by citing examples in reality is a fruitless endeavour.

People often say a dog is a dog, and not a cat - 0.999~ is 0.999~ not 1. This is absolutely true. Does this mean their is a contradiction in reality? Certainly not! You'll find that there is no such thing as 0.999~ it's an abstraction, you cannot in reality have an infinite number of things such as decimal places. If you do, you can only work on these theoretically, and they shouldn't be applied to reality because, contradictions will arise. 0.999 does not = 1, no matter how many finite number of 9's you attach on the end of it, it will NEVER = 1 - try it out for your self. The ONLY way it equals 1 is when you put an abstract infinite number of 9's on it.

When you apply abstract concepts to reality, do not be surprised if you find anomalies, it's like applying real-life to a game or television show - it's obviously different.

 

[Imagine]

Theoretically 0.999 recurring does = 1. However, to therefore say this is wrong by citing examples in reality is a fruitless endeavour.

People often say a dog is a dog, and not a cat - 0.999~ is 0.999~ not 1. This is absolutely true. Does this mean their is a contradiction in reality? Certainly not! You'll find that there is no such thing as 0.999~ it's an abstraction, you cannot in reality have an infinite number of things such as decimal places. If you do, you can only work on these theoretically, and they shouldn't be applied to reality because, contradictions will arise. 0.999 does not = 1, no matter how many finite number of 9's you attach on the end of it, it will NEVER = 1 - try it out for your self. The ONLY way it equals 1 is when you put an abstract infinite number of 9's on it.

When you apply abstract concepts to reality, do not be surprised if you find anomalies, it's like applying real-life to a game or television show - it's obviously different.

I agree to some extent, but I also disagree. We see .999... recurring all the time. We just like to call it 1, or one whole. .999... to 1 is the same as 2/4 to 1/2. They are different names for the same thing.

Also, it is indeed possible to have the infinitely recurring number, but one must create it themselves, not measure it. We use infinite numbers and limits in calculus all the time to find the area of curves, why are we suddenly not allowed to do it to simple numbers?

 

[malakadang]

I agree to some extent, but I also disagree. We see .999... recurring all the time. We just like to call it 1, or one whole. .999... to 1 is the same as 2/4 to 1/2. They are different names for the same thing.

We just round it for simplicity much like we put 0.999... for simplicity.

Also, it is indeed possible to have the infinitely recurring number, but one must create it themselves, not measure it. We use infinite numbers and limits in calculus all the time to find the area of curves, why are we suddenly not allowed to do it to simple numbers?

I've never done limits in calculus, however, I think that infinite used in these calculations is merely an abstraction - it denotes a very very very large number. I've used the symbol infinite in other forms of mathematics, statistics namely, and if you replace the symbol with a very very very large number (9999999999999999999) the result is unchanged. The symbol infinite is not a real number, it doesn't obey the laws of arithmetic like real numbers do.

Also, I'm not saying you're not allowed use it on simple numbers. You can, but then you shouldn't be surprised if your results are seemingly contradictory to reality. Let's not forget that 0.999 with any finite number of 9's is an entirely different number from 1.

 

[Imagine]

We just round it for simplicity much like we put 0.999... for simplicity.

Yes, but we also simplify 1024/2048 into 1/2 for simplicity. It doesn't mean that they are different numbers. They are equivalent.

I've never done limits in calculus, however, I think that infinite used in these calculations is merely an abstraction - it denotes a very very very large number. I've used the symbol infinite in other forms of mathematics, statistics namely, and if you replace the symbol with a very very very large number (9999999999999999999) the result is unchanged. The symbol infinite is not a real number, it doesn't obey the laws of arithmetic like real numbers do.

Well yeah, it doesn't obey the laws of arithmetic, but we aren't really doing anything with infinity here, the 9 just has an infinite number of recurring decimal places. At this point, we haven't yet multiplied, divided, added, or subtracted infinity. (Or any other operation of it).

Also, I'm not saying you're not allowed use it on simple numbers. You can, but then you shouldn't be surprised if your results are seemingly contradictory to reality. Let's not forget that 0.999 with any finite number of 9's is an entirely different number from 1.

Of course, I don't disagree with that.

 

[malakadang]

Yes, but we also simplify 1024/2048 into 1/2 for simplicity. It doesn't mean that they are different numbers. They are equivalent.

Yes, but, 0.999 (with any finite number of 9's) over 1 is not 1/1.

Well yeah, it doesn't obey the laws of arithmetic, but we aren't really doing anything with infinity here, the 9 just has an infinite number of recurring symbols. At this point, we haven't yet multiplied, divided, added, or subtracted infinity. (Or any other operation of it).

Does the number line extend to infinity?