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Does 0.999... equal 1?

Does 0.999... equal to 1?

  • Of course

    Votes: 43 27.9%

  • No wai

    Votes: 111 72.1%
  • Total voters
    154
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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!
300px-999_Perspective.png
 
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.
equation1.gif


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:
9s_thirds


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?
 
WhereIsTheGod said:
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?
Click to expand...

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.
 
isosceles said:
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.
equation1.gif


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:
9s_thirds


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.
Click to expand...

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.
 
my math teacher said no.

:P
 
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?
 
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