Does 0.999... equal 1?

You could say any number >0.5 rounded up = 1.
0.999... Does not = 1
9/9 as a fraction is a division of itself and would = 0 if expressed as a decimal!

 

zero is also infinitely small

 

No, zero represents nothingness. An infinitely small number is 0.00...001.

 

I am reconsidering, but I still believe the algebra.

And I have seen quite a few misconceptions about decimals/rounding on this thread. We aren't talking about .999. Yes, we all know that doesn't equal 1.

Also, there is a way to display 1/3 (1/6, 1/9, etc) in decimal form.


Anyway, I have seen several proofs (most of which have already been posted). If you can show my why the algebra doesn't work. I will change my mind.


Even intuitively, this is true:


This is one of the most complete explanations I've seen. Go here: http://polymathematics.typepad.com/photos/uncategorized/9s_thirds.

Oh, x9, you mentioned that calculus holds more information about this. I have taken calculus and I was wondering if you could be more specific.

 

Let's say you have function y. The slope of function y is Ay/Ax (pretend the A is a delta symbol). Take the lengths of Ay and Ax to an infinitely small value, but not zero. You get dy/dx, which is the derivative.

dy and dx are infinitely small.

All of calculus is based on the infinitesimal... isn't it?

 

In short, yes.

.999... is a constant though, not a variable.

 

The difference between 1 and .99999... is essentially the length of dx.

We want it to be zero, except that you can't divide by it.

 

Fractions cannot be fully represented by decimals.

 

If you want to really get into it...

Numbers can't really be represented by numeral tokens at all.

I'll edit this post when/if I ever get high.

 

Technically, no.

But in a way..it is..

Like others have said, there are flaws in math..

 

This is the precise decimal representation of 1/3.

Bah. Can't really see it. Here: http://alt2.artofproblemsolving.com.../c2dd9f97319f8fa5438fe07c4cab8518026f94ab.gif

 

Wow, if 1/1 <> 1, then 1 <> 1. And if 1 doesn't equal itself, then it shouldn't exist.

 

It's still not precise. That just extends the 3's on forever.

 

QED

That IS 1/3.

 

Also...

3/3 = 2/2 = 1/1 = 1

1/3 = .333 repeating

2/3 = .666 repeating

3/3 = .999 repeating

Decimals and fractions are totally different though...


Oh ^_^ Tarren just said that

So..I guess it could be classified as both...

 

my math teacher said no.

 

3/3 = 1

Are you kidding me?

 

Well, 3/3 DOES equal one, but it sorta does actually equal .999 repeating, but everyone rounds it to 1, which is what you are supposed to do..which makes 3/3 equal one and .999 repeating.

 

Were not rounding anything here. It doesn't sort of equal .999 because sort of equal doesn't exist in math.

 

1/3 does not = .333.. .333... is just the closest way we can represent 1/3.

My Thoughts.

3/3 = 1
2/3 Does not = .666(repeated)


Get me?