Does .999... = 1?

Discuss, wise nerds of AT!

lol if you write it that way then NO!

does 1/0 = .999.../0?

It depends on the amount of significant digits you are searching for within your statement

Yes it does.

X=0.99999
10x=9.99999
10x-x=9.99999-.99999
9x=9
x=1

Or
(1/9)=0.11111
9*(1/9)=9*0.11111
1=0.99999

It doesn't depend on anything .9 repeating = 1

If you write it that way then yes...

.9999 repeating is not 1

1/9 * 9 = 9/9 = 1 is the correct way of doing it.

That's just a flaw in the different mechanisms of math. Like X/0. That is why we have our general theory and then exceptions.
But it doesn't matter because we are infinitely close so it's just a matter of opinion.

If 0.999 repeating is = 1 then you might as well say we can get a space ship to achieve the speed of light. Even if we can collect a vast amount of antimatter to power the ship we can only get infinitely close.

So is 0.0000000... repeating = 0?

At infinity, 0.9999... would be equal to 1. If we're only talking about "infinitely close", then we're not at infinity yet. And that really is the crux of the matter of understanding what infinity is.

What is this nonsense about the speed of light?

1/9=.111... 9*1/9=9/9=1 .111...*9=.999... =9*1/9=1

Also, the word you are looking for is infinitesimally

The amount of energy required to gain more speed exponentially increases as you get closer to the speed of light because as you mover faster and faster you gain mass, it comes to the point where you need an infinite amount of energy to increase your speed to the speed of light.

Say this is true. How does that relate to his argument?

the nonsesnse is an analogy. People use analogies to help other people understand a point.

Yes because the forumla is exponential. Pretty much as long as you have mass, it is impossible. Some people argue a photon has mass but it is really just energy. Then again, if you look into the "strings" theory then everything is energy. FML fluff physics, it's evolving faster than AIDS.

ttt, nobody has gotten this correct yet

As things stand, it seems like your analogy makes no sense. I am happy to forget about it though =P

i guess it makes you the only one it doesn't make sense to. But it was obvious to me what your goal was since your first reply.
By your argument, you might as well say that

women = square root of all evil = mathetically correct

or

we might as well say PI is 22/7...

If you can actually say x=.99999...
then you can't say x = 1 int he same equation/problem
X cannot be 2 different value regardless of how close they are. X is a variable, but it is 1 variable, not 2 or more.

Actually tduong, .999 repeating is 1.000 (repeating 0's). It is the proper decimal representation for the real line. It is not two different values, it is two different representations. In the same sense, 1/3 = .333 repeating. There is no problem if X = 1/3 and X = .333... it is not two values, it is two representations of the same value.

I think that many mathematically minded people would disagree with your analogy.

Because he is saying that no matter how many repeating .9999999 you have it is never 1. You can be infinitely close to being one if the .9999999 keeps repeating forever but it never reaches one no matter how many digits it goes. just like how we can get infinitely close to the speed of light but in theory we can never reach the speed of light I could be way off base but I think that is what he was getting at.

real analysis proves that .99999 repeating is the same as 1.
it's not a limit or anything. It is to prove that our representation of real numbers is not unique.

This isn't opinion, this is generally accepted mathematics.

You can agree or disagree with it all you like.

http://math.stackexchange.com/questions/11/does-99999-1
http://en.wikipedia.org/wiki/0.999...
http://polymathematics.typepad.com/...6/06/no_im_sorry_it_.html
http://www.mathdb.org/...ementary/number/ne_N1.pdf

If you want to redefine the assumptions behind set theory then .99999 can be anything you like.

also

http://mathworld.wolfram.com/RepeatingDecimal.html
http://mathforum.org/dr.math/faq/faq.0.9999.html

I was just explaining why he might say that... Also I suck at math, why do you think I studied Economics in college? No hard math required :p

martian beat me to the punch. Approaching the speed of light is a limit issue. On the other hand .999... = 1

If anyone believes that 0.999999... repeating infinitely is not equal to 1, then you basically don't understand what "infinite" is.

It's like talking about the asymptote of the y = 1/x graph. As x increases, y gets closer and closer to 0. Yes, y never quite reaches 0, but that's because x is never a value that is at infinity because there is always another value larger than it.

But if x is hypothetically at the impossible value of infinity, then y would be equal to 0. And that's the key to understanding the matter, to understand that if 0.999999 is really repeated to infinity, it would be equal to 1.

Ok; like i said i suck at math but i got why he at least brought it up.

That makes since to me, but if it is impossible for x to be at infinity why can we say y = 0? would the impossibility of x being at infinity make the possibility of y = 0 impossible too?

it does not make sense on calculations though.
it depends on the what is the usage of the calculation.
but 0.99999.... to the infinity would surely be equal to 1 approached from the left side

does -x = x ?

answer http://youtu.be/yxOIQy7VGPs

Whatever, I can prove it's not equal just as you can prove it is equal. I know it's generally accepted as 1 but to me, it is not. We all know that. Everything we know in math and science is only what is observable to our eyes. Even our math system is imperfect and therefore we created exceptions.

We all know that the only people who ever made breakthroughs in physics and mathematics are always regarded as weird(to put it nicely). I'm not saying i'm some brilliant mind because i'm not but you are bashing me for not embracing your generally accepted way of thinking. It's 2012, get over yourself and soften that epeen.

The truth is we, as humans, will never be able to grasp what infinite is. We accept it as a concept and we're fine with it because we don't know what else to do with it. If infinity exist, then can you prove that space goes on forever? We can't prove that space is infinite or finite. Both directions are theories at best.

Have any of you ever thought about your place in the universe? We're basically less than a spec of dust that existed in less than a fraction of a blink in time. We're not sure if time and space is an illusion or not. The only thing we know is how to measure it. We used to think that space is empty or nothingness and now we know it's not. Now space is linked with time and both and be bent/warped. We generally accepted that there are only 2 things in the universe that exist within time and space and it is matter and energy. Now a new way of thinking that everything is really just energy is starting to be accepted.

My point is stop being so close minded. What you learn in school and is generally accepted may be changed tomorrow. I don't understand why they still teach Newton's law of gravity in school since it has been proven to be inaccurate several times and better theories have been accepted.

0.9... is, by definition, a rational number. A rational number, by definition, can be expressed as a fraction a/b of two integer numbers. Justtaint showed how it's done but he came to 0.9...=9/9.

If 0.9... is not 1 then can you give an example of a and b (a being not equal b) that gives you 0.9...?

@tduong: that's true for science.
Mathematics is not a science though, it's actually form of philosophy/logic based on a set of rules (actually a very simple set of rules) from which everything we know and will deduce from it is based. the .99999... = 1 is used as an illustration that based on our rules, numerical representation is not unique.

"Infinity" in mathematics is actually a set. There are different kinds of infinities and the number of infinities is infinite although we cannot tell which kind of "infinite" the infinite number of infinities is.
For example 1,2,3,4,... is one type of infinity
all the real numbers is another type of infinity. They are not the same. In fact all the real numbers is a "larger" set of infinity than the first.
We have defined these rules and concepts to help us solve real world problems (and debate philisophical questions), but it's still a tool of our own making and is our proxy for reality when we do science.

(short version: science is deductive, math is inductive)

You really don't understand why Newton's Law of Gravity is taught in school?

Newtons law of gravity works well for smaller objects but it can fall short when it comes to very large and dense objects. For things like that Einsteins theory of general relativity is better suited. Although Newtons laws are not perfect, it is a great basic concept and set of principles to learn for children.

Gravity is like the glue that binds the cosmos together, and to be completely honest we still don't understand it completely.

true it is not but at the same time it is a direct 2 way relationship. We cannot prove science work without math and we cannot prove math work without science.

I'm not saying it shouldn't be taught, i'm saying it shouldn't be taught as a law because it is obviously very flawed.

I'm Slash, hence my signature.

i'm pretty sure that's a whole bunch of BS as gravity is never mentioned in the bible

Hey you can believe whatever you want Trife :)

If 0.999... and 1 are not equal, then it should be a trivial matter to show me a number which falls between the two.

To show how many times this issue has been rehashed on AT (which I love every time btw), I remember that this is the (valid) point you always use.

<3 MATH BUDDIES <3

And what do you want it to be taught? As Newton's hypothesis? LOL
That's why it is just a law

get a room, nerds.

the statistics you learn in highschool/intro is also not completely correct and has been replaced with better theories too. The point is that you start with the simpler version and work your way up to the more complex. Newton's theory was the basis for everything that follows.
I saw theory because in science you can never prove something absolutely (unlike mathematics where you can).

@Trife: only if that room has you tied to the bed.

i've been tied up for like a week and a half now

but what is even sadder is that i'm still not sure if .999... = 1 or not

7.56248=1


Want proof?
7.56248=1x

Btw .999...=.999...
1=1

I wish somebody would argue this in person, id fight them

1 + 1 = 10

QFT

y is this thread so nerdy?!

yes, and this thread pops up at least once a year