Support NeoGAF

[zoku88]

To be fair though, a negative charge is just an arbitrary assignment of one to be negative and one to be positive. There is nothing inherently "negative" about a negative charge, it was more that we can very easily understand (from mathematics) the idea of negative and positive canceling each other out, so we assigned them in such a manner.

Well, I think it's enough to say that they both can't have the same sign.

 

[2San]

Ok work with me I haven't done real math's since going to Uni(I do economics now math is for pussies over here ), but wasn't it so that you just don't use infinites in calculations. That's pretty much the first thing you learn. The only time you do is when you address limits(and even then it's an approximation). Not to mention we are unable to process infinite and never will. Even if you someway prove it's true it's irrelevant since, it has no application in real life. So it's pretty much a MOO discussion.

Btw the Fractions and long division proof is invalid from the start, normally you'd think is that you can't approach fractions with infinites, it's just a really good approximation. So 1/3 =/= 0,333... not that 0,999...=1

 

[Pyke Presco]

True, but again, saying they dont have the same sign is appealing to mathematics (something we understand) to give a model of things in the real world. But, since that is something mathematics is really good at doing, it all works out.

Also, I'm a little bitter that my last explanation is buried at the bottom of the previous page. Go read it Godzilla!

 

[zoku88]

Ok work with me I haven't done real math's since going to Uni(I do economics now math is for pussies over here ), but wasn't it so that you just don't use infinites in calculations. That's pretty much the first thing you learn. The only time you do is when you address limits(and even then it's an approximation). Not to mention we are unable to process infinite and never will. Even if you someway prove it's true it's irrelevant since, it has no application in real life. So it's pretty much a MOO discussion.

Btw the Fractions and long division proof is invalid from the start, normally you'd think is that you can't approach fractions with infinites, it's just a really good approximation. So 1/3 =/= 0,333... not that 0,999...=1

Sorry, but that was all incorrect. No approximations.

Even the applications part is incorrect. You could argue that you need to keep all of this in mind when you make calculators (like, when you had 1/3 + 1/3 + 1/3 on a computer.) You wouldn't want to accrue errors do to messed up calculations of that kind.

 

[Pyke Presco]

Ok work with me I haven't done real math's since going to Uni(I do economics now math is for pussies over here ), but wasn't it so that you just don't use infinites in calculations. That's pretty much the first thing you learn. The only time you do is when you address limits(and even then it's an approximation). Not to mention we are unable to process infinite and never will. Even if you someway prove it's true it's irrelevant since, it has no application in real life. So it's pretty much a MOO discussion.

Btw the Fractions and long division proof is invalid from the start, normally you'd think is that you can't approach fractions with infinites, it's just a really good approximation. So 1/3 =/= 0,333... not that 0,999...=1

Actually, 1/3 is exactly equal to 0.333(repeated), and 0.999(repeated) is exactly equal to 1. That is the entire argument that has been spanning the last 9 pages. There is nothing "approximate" about those representations, they are exact.

The only reason they look so funny is because you are trying to present an exact number with a decimal expansion. If you stop the expansion somewhere, say at 1/3=0.33333 then yes, you only have an approximation. But if you let it go to an infinite number of decimal places it is no longer an approximation. It is an equality. The problem is there is no way for us to write an infinite number of digits on the page, so we have to leave it cut off at some point, and let you visualize it going to infinity in your head. Since this is impossible to do (you cannot see infinity, only have a theoretical understanding of it) people get hung up on the 6 digits or so presented to them and think its therefore not the same thing.

 

[2San]

Yup you guys are right, meh wasted a decent 5 minutes on thinking on that. :lol

Again we don't use infinites in algebra. Why do you think why we can't divide by zero? Because it's left undefined. Sure you can if you change the definition what is zero it is changeable to suit your needs. But if you change definition to what is zero are the standard rules still applicable? With the standard rules you can't calculate with infinite and if you attempt to why do you think you can use the standard rules to prove the problem?

You guys mention it yourself we can't process infinite hence we can never have a clear understanding about it. Thus making claims about infinite is outrageous from the start. It's like trying to grasp a cloud with math. xD

 

[Tntnnbltn]

Again we don't use infinites in algebra. Why do you think why we can't divide by zero? Because it's left undefined. [...]

There's a difference between 'infinity' as a number, and 'infinite' with respect to trailing decimals.

I mean really, every single "finite" number possible actually has 0 as an infinitely recurring decimal.

 

[iapetus]

Again we don't use infinites in algebra. Why do you think why we can't divide by zero?

Because most values you could assign to the result of a division by zero lead to inconsistencies in other basic maths.

 

[Pyke Presco]

Well, we use infinity to help us understand mathematics in many ways. For example, when taking limits, or for use in calculus with integrals and differential equations. We have defined infinity in such a way that it is larger than all possible positive numbers, and mathematics dealing specifically with infinity tends to get a little crazy. For example:
infinity+infinity=infinity
infinity*infinity=infinity

It is impossible for us to get a larger number than infinity; even when multiplied with itself we still get the same value. And when you add it to itself, you still get the same number, something typically reserved for zero. It's just the point at which our conventional understanding of the number system breaks down a little. But that doesnt make it useless to us!

We could have just as easily defined infinity as something else, something it is possible to visualize (like say, 1 with a billion zeroes following it). If we had done so, it wouldnt be valuable to us at all; it would just be another number. It would be a really, really big number, but it still wouldnt help us the way it does with infinity defined as it is.

It's not outrageous for us to use infinity, we just need to have a clear understanding of what it is before we go crazy with it and apply it to all our mathematics.

 

[2San]

It's not outrageous for us to use infinity, we just need to have a clear understanding of what it is before we go crazy with it and apply it to all our mathematics.

Hence my point this discussion is pointless since we don't have a clear understanding to what infinity is. Unlike other sciences maths is something where we don't like inconsistencies.

There's a difference between 'infinity' as a number, and 'infinite' with respect to trailing decimals.

I mean really, every single "finite" number possible actually has 0 as an infinitely recurring decimal.

Even if they are different, doesn't mean we can grasp infinite, so it's weird we can use it to make calculations and as you can see if you try to use it fails or the standard math rules fail. Rather then thinking that the standard rules are wrong, I'm inclined to believe our basic understanding to what infinite is wrong.

 

[Pyke Presco]

But we do have a clear understanding of it, at least in the sense of how we have defined it. It is an unbounded value with no limit, that is larger than all positive numbers(or when negative, smaller than all negative numbers). We can use it as a number, but it is not a number in the same sense that 1 or 976 are numbers. It is a mathematical concept that we can make use of in certain situations.

It's no different than using integers in some situations and real numbers in others. Both are valuable and both have their place, just like infinity. A problem that requires real numbers to solve can not necessarily be solved with integers, but that doesn't mean that integers are some non-understandable concept that we therefore shouldn't use.

tntnnbltn: I am pretty sure 2san is discussing infinity (the value) which is a tangent to the thread, but since some explanations for the topic at hand have used infinity (specifically mine on the last page, which I think is what he was responding to) I still would consider the discussion relevant to the topic.

 

[Tntnnbltn]

Even if they are different, doesn't mean we can grasp infinite, so it's weird we can use it to make calculations and as you can see if you try to use it fails or the standard math rules fail. Rather then thinking that the standard rules are wrong, I'm inclined to believe our basic understanding to what infinite is wrong.

You still haven't defined whether you are objecting to infinity as a number (which is understandable), or numbers that have an infinite number of decimal places (which is what 99% of this thread is about).

 

[2San]

But we do have a clear understanding of it, at least in the sense of how we have defined it. It is an unbounded value with no limit, that is larger than all positive numbers(or when negative, smaller than all negative numbers). We can use it as a number, but it is not a number in the same sense that 1 or 976 are numbers. It is a mathematical concept that we can make use of in certain situations.

It's no different than using integers in some situations and real numbers in others. Both are valuable and both have their place, just like infinity. A problem that requires real numbers to solve can not necessarily be solved with integers, but that doesn't mean that integers are some non-understandable concept that we therefore shouldn't use.

Yeah and the clear understanding is don't use them.
I don't know how it is in other countries, but in the Netherlands. I had classes where we learned how to prove the mathematical rules. You know we use letters. Even with calculations we where not allowed to used decimal numbers in any case. Since they are inaccurate, there is an error that exists when you use them. In this case the error is infinitely small, but still not zero. Thus the conclusions you pull with them always have an error in them even if it is infinitely small. We can use decimals, but it will always be less accurate then not using them. This discussion spured from ignoring that error.

This whole discussion revolves around that small error. You can do what you want, but I doubt it will ever be applied for several reasons.

 

[Pyke Presco]

Yeah and the clear understanding is don't use them.
I don't know how it is in other countries, but in the Netherlands. I had classes where we learned how to prove the mathematical rules. You know we use letters. Even with calculations we where not allowed to used decimal numbers in any case. Since they are inaccurate, there is an error that exists when you use them. In this case the error is infinitely small, but still not zero. Thus the conclusions you pull with them always have an error in them even if it is infinitely small. We can use decimals, but it will always be less accurate then not using them.

You're absolutely right, using a decimal approximation will result is errors. But the topic at hand is that 0.999(repeated) is in fact not a decimal approximation at all but is in fact equal to 1 (which it is, as long as you allow for an infinite number if 9s, which seems to be your main concern with the solutions provided thus far.

And it seems that you don't accept infinity on a primal level, as if you don't "believe" in it, which is utterly ridiculous. This is mathematics, we are not asking you to take anything on faith. The only way that the solutions work when involving infinity is that you accept infinity as a mathematical concept the way it is commonly defined by mathematicians. If this is not permissable to you, then there is absolutely no way for us to convince you that our solutions are correct, since you are not accepting the mthemtics we are using. Imagine if you asked us to find the value of 3/2 but refused to work in anything other than an integer number system. Without rational/real numbers, 3/2 does not exist and so if you only accept the integer number system we simply cannot explain what 3/2 is.

You have to accept the real numbers ( and infinity) for us to show that 0.999(repeated to infinity)=1. If you don't then there is absolutely no way for us to convince you.

 

[Inflammable Slinky]

You're absolutely right, using a decimal approximation will result is errors. But the topic at hand is that 0.999(repeated) is in fact not a decimal approximation at all but is in fact equal to 1 (which it is, as long as you allow for an infinite number if 9s, which seems to be your main concern with the solutions provided thus far.

And it seems that you don't accept infinity on a primal level, as if you don't "believe" in it, which is utterly ridiculous. This is mathematics, we are not asking you to take anything on faith. The only way that the solutions work when involving infinity is that you accept infinity as a mathematical concept the way it is commonly defined by mathematicians. If this is not permissable to you, then there is absolutely no way for us to convince you that our solutions are correct, since you are not accepting the mthemtics we are using. Imagine if you asked us to find the value of 3/2 but refused to work in anything other than an integer number system. Without rational/real numbers, 3/2 does not exist and so if you only accept the integer number system we simply cannot explain what 3/2 is.

You have to accept the real numbers ( and infinity) for us to show that 0.999(repeated to infinity)=1. If you don't then there is absolutely no way for us to convince you.

Actually, if you accept the integer set exists, doesn't that mean real numbers exist? I recall from discrete math that we had to prove the existence of the real set using only Z (integer set)

 

[2San]

You're absolutely right, using a decimal approximation will result is errors. But the topic at hand is that 0.999(repeated) is in fact not a decimal approximation at all but is in fact equal to 1 (which it is, as long as you allow for an infinite number if 9s, which seems to be your main concern with the solutions provided thus far.

And it seems that you don't accept infinity on a primal level, as if you don't "believe" in it, which is utterly ridiculous. This is mathematics, we are not asking you to take anything on faith. The only way that the solutions work when involving infinity is that you accept infinity as a mathematical concept the way it is commonly defined by mathematicians. If this is not permissable to you, then there is absolutely no way for us to convince you that our solutions are correct, since you are not accepting the mthemtics we are using. Imagine if you asked us to find the value of 3/2 but refused to work in anything other than an integer number system. Without rational/real numbers, 3/2 does not exist and so if you only accept the integer number system we simply cannot explain what 3/2 is.

You have to accept the real numbers ( and infinity) for us to show that 0.999(repeated to infinity)=1. If you don't then there is absolutely no way for us to convince you.

I believe in infinite, how ever I'm skeptical in using it since it leads to inconsistencies. Like I mentioned before with dividing by zero. It exists a/0, but what it leads to is undefined. Some say you can, some say you can't all based on how you define zero.

Yeah so in the end whether this is true or not is, is how you define infinite. Like dividing by zero for basic math it's irrelevant.

 

[Pyke Presco]

Slinky: I am not sure whether that is the case or not, but assume for a moment that even if it were true, it was denied by whomever you were trying to convince. It would be impossible to go any further, since the fundamentals of your mathematics are denied outright.

However, 2san just said he does accept infinity, he just doesn't like the inconsistencies that result from using it. I have no problem with that in basic mathematics(which I take to mean algebra, as that was his initial argument for where infinity was unnecessary), since infinity is a little abstract. But the problem at hand is NOT basic mathematics. It deals with infinity right from the outset, since 0.99(repeated) has infinite 9s. Therefore we need to have a definition for infinity to even formulate the problem in the first place! Thus,I don't see how one can object to using infinity in the solution as well.

 

[2San]

Lol just noticed this was all discussed in the first page. Wow way to waste my time. xD

 

[desh]

Lol just noticed this was all discussed in the first page. Wow way to waste my time. xD

So, does this mean you understand now?

 

[Cyan]

So it's pretty much a MOO discussion.

...huh?

 

[jas0nuk]

You need to be precise with your question
0.9999, as mentioned in your post, is in the set of rational numbers Z, (0.9999 = 9999/10000). It is definitely not equal to 1.

0.999... on the other hand:
x = 0.999...
10x = 9.999...
9x = 10x - x = 9.999... - 0.999... = 9
x = 1
The ... denotes that the the 9 repeats indefinitely which means that 0.999... is actually a natural number.

Also, you can't "not accept" infinity, it's quite an accepted part of maths, used heavily in calculus. You just have to use some logic to define a few operations on infinity
e.g. (for x > 0) ∞ * ∞ = ∞
∞ + x = ∞
∞ - x = ∞
-x * ∞ = -∞
∞ - ∞ and ∞/∞ are undefined
∞ > x, for all x in R.

∞ is a number greater than any other, basically.

Also, x/0 != ∞. Division by zero is an undefined operation. You can refer to ∞ using other methods, e.g. lim x->0 1/x^2 = ∞

 

[Raistlin]

The only repeating decimal in that calculation is 1.000_, you haven't finished solving it to know the .333 is one too.

So wait a minute, you concede that 1.000... is a repeating decimal, but won't acknowledge that 1/3 in decimal form is a repeating decimal?

Do you think at some point the long division will just magically change? :lol

 

[Ashes]

okay this is getting absurd. No matter what equation/formula/fraction/whatever you do, the answer 0.9999...=1 holds true. Whoever disagrees should show their math from here on in.... This (and math) isn't about opinions, its about comprehension and lack thereof.

For the doubters... on a similiar matter....

why is this nonsense?> 0.0000000000infinity zeros then 2 (hint: note the infinity zeros means that the 2 never comes lol. Its so simple...)

 

[desh]

The detractors have stopped posting, so I think it's safe to say that this topic is closed (for now...).

 

[Anaxagoras]

Sorry for the bump, but I just discussed this topic with my math teacher and he insisted that 0.999.. is not equal to one, and his argument was that no matter how infinitely small the difference is it is still there.
So I asked him to calculate the difference for me and he of course couldn't but he still insisted that it is still there.
I really don't know how to convince him but I guess I am kind of giving up on it.

 

[C.Dark.DN]

Sorry for the bump, but I just discussed this topic with my math teacher and he insisted that 0.999.. is not equal to one, and his argument was that no matter how infinitely small the difference is it is still there.
So I asked him to calculate the difference for me and he of course couldn't but he still insisted that it is still there.
I really don't know how to convince him but I guess I am kind of giving up on it.

high school teacher or college professor?

 

[Anaxagoras]

high school teacher or college professor?

High school, I have had better teachers than him.

 

[C.Dark.DN]

High school, I have had better teachers than him.

does he teach calculus? somewhere in your school someone is teaching limits in a calculus class. and that concept explains the equality.

 

[Shao Kahn Brewing a Stew]

Sorry for the bump, but I just discussed this topic with my math teacher and he insisted that 0.999.. is not equal to one, and his argument was that no matter how infinitely small the difference is it is still there.
So I asked him to calculate the difference for me and he of course couldn't but he still insisted that it is still there.
I really don't know how to convince him but I guess I am kind of giving up on it.

But he is right. 0.9999..... is not equal to one!There's infinity, and then there is infinity + 1


That said, Laplace transformations and L'Hospital's Rule does wonders...

THAT SAID, here is the proof that will convince your prof:

0.3333333....... = 1/3
0.3333333....... x 3 = 1/3 x 3
0.9999999....... = 1

 

[C.Dark.DN]

But he is right. 0.9999..... is not equal to one!There's infinity, and then there is infinity + 1


That said, Laplace transformations and L'Hospital's Rule does wonders...

THAT SAID, here is the proof that will convince your prof:

0.3333333....... = 1/3
0.3333333....... x 3 = 1/3 x 3
0.9999999....... = 1

it's better to just prove it using limits.

 

[Anaxagoras]

does he teach calculus? somewhere in your school someone is teaching limits in a calculus class. and that concept explains the equality.

I graduated, I am just taking some extra courses at a school for people who didn't make it or need extra points to continue studies, I doubt that I will find one, but if I read enough myself I can provide him with a page that proves it, I doubt that he would be close minded about it.

 

[Nexus Zero]

Sorry for bumping this thread but I've been having a "think" and I was wondering if this implies that it is possible to travel at the speed of light, if not for all intents and purposes?

 

[Rapstah]

1/0 is infinitely large, but is 0/0?

 

[firehawk12]

It's been a while, but in terms of analysis, 0/0 proves that a limit exists for certain fractional functions. L'Hopital's Rule or something like that.

Sorry for bumping this thread but I've been having a "think" and I was wondering if this implies that it is possible to travel at the speed of light, if not for all intents and purposes?

Only if you can generate a constant velocity of 0.9999999...c indefinitely, I suppose?

 

[grumble]

1/0 is infinitely large, but is 0/0?

1/0 is undefined, not infinite. Same with 0/0.

 

[fredrancour]

Only if you can generate a constant velocity of 0.9999999...c indefinitely, I suppose?

I don't think so. .999=1. thus .999c=c, which is as far as we can tell impossible. You can't use semantics(or whatever the equivalent concept is for math expressions) to break the laws of physics

 

[firehawk12]

I don't think so. .999=1. thus .999c=c, which is as far as we can tell impossible. You can't use semantics(or whatever the equivalent concept is for math expressions) to break the laws of physics

Oh yeah, I know. I'm just making an uninformed guess/thought experiment.

I mean, even in a theoretical context, it's impossible to reach a speed of 0.9999...c?

 

[KittyKittyBangBang]

Here's another one:

1/9 = .1111111111111111...
2/9 = .2222222222222222...
3/9 = .3333333333333333...
4/9 = .4444444444444444...
...
8/9 = .8888888888888888...
9/9 = 1

MIND BLOWN, didnt realize this

I think the fraction arguement (1/3+2/3=3/3)is the easiest to understand why .99999999999 is equal to 1

 

[Mudkips]

.999... is not 1.
.999... is our inexact representation of an infinite series of 9s.

1/9 is represented as .111...
1/9 * 9 = 1

.111... * 9 = .999...

But .999... is not 1/9 * 9.

You cannot perform operations on an imprecise representation of a value without the end value being as imprecise.

Edit: Fuck, old thread is old.

 

[bachikarn]

Sorry for bumping this thread but I've been having a "think" and I was wondering if this implies that it is possible to travel at the speed of light, if not for all intents and purposes?

Why would you think this?

 

[zoku88]

.999... is not 1.
.999... is our inexact representation of an infinite series of 9s.

1/9 is represented as .111...
1/9 * 9 = 1

.111... * 9 = .999...

But .999... is not 1/9 * 9.

You cannot perform operations on an imprecise representation of a value without the end value being as imprecise.

Edit: Fuck, old thread is old.

Yup, argument is old and wrong.

 

[Korey]

.999... is not 1.
.999... is our inexact representation of an infinite series of 9s.

1/9 is represented as .111...
1/9 * 9 = 1

.111... * 9 = .999...

But .999... is not 1/9 * 9.

You cannot perform operations on an imprecise representation of a value without the end value being as imprecise.

Edit: Fuck, old thread is old.

You're wrong, and there are 9 pages + wikipedia + any high school math teacher to prove it to you. Why did this have to be bumped T_T

 

[Magni]

-nvm

 

[Zio]

ooooh...page 9!!!

:lol

 

[koam]

ooooh...page 9!!!

:lol

50 posts per page is fail

 

[Feep]

.999... is not 1.
.999... is our inexact representation of an infinite series of 9s.

1/9 is represented as .111...
1/9 * 9 = 1

.111... * 9 = .999...

But .999... is not 1/9 * 9.

You cannot perform operations on an imprecise representation of a value without the end value being as imprecise.

Edit: Fuck, old thread is old.

Dude, you are such a dick today. Flashmobs and now this? :lol :lol :lol