Does 0.999... equal 1?

Yes, with the limit set at 1, as x approaches one, its values jump higher and higher. Yet, at 1 itself, it is undefined.[/quote]

isosceles, to have .33 repeating accurately represent 1/3, you would have to extend it into infinity.

Now, if you multiply .33 repeating by 10, you get 3.33 repeating, with a zero on the end.

 

It does. By convention we express those numbers in a unique way - but what you said is still true.

Looking at it from another aspect - what's the length of a point? That is how much 1 exceeds .99999...

 

not really i know it says that but thats in a fraction.

 

That's exactly it! The difference between the two is infinitely small, so realistically, practically, they are the same, but theoretically, they are not.

 

So, you are saying that by multiplying it by 10, it no longer repeats infinitely? I'm afraid that doesn't work. Such an operation simply shifts the decimal point.

 

There is no zero at the end. The 3s extend to infinity. NOTHING comes after those 3s. In order to have something other than 3 at the end of those 3s repeated to infinity you would have to define infinity as a real number and that just isnt right...

There is no number between .999... and 1. They are theoretically the same.

 

I think that proves it right there, if nothing else does.

No number exists between .999999... and 1.

 

You cannot shift infinite numbers to the left by one, and then perform simple mathematics upon it.

 

Yes, that is a property of infinite numbers.

Your still thinking in terms of finite numbers. Your saying that ∞ - 1 ≠ ∞ but they infact do equal. you can do that with any finite number.

∞ = ∞ + 999999999999999999999999999
∞ = ∞ - 999999999999999999999999999
∞ = ∞ * 999999999999999999999999999
therefore
10 * .111... = 1.111...

 

Infinity is not a number in itself, it is just a concept.

 

Infinity is the concept of being bigger than any real number.

.999... extends to infinity. Your saying that 9.999... stops at the point on less than .999... which is bad logic. You cannot proform the same mathmatics on it you can with numbers.

 

I'm not saying that, I'm saying that you cannot very well multiply infinity by a number.

 

Infinity is larger than all real numbers. Two times infinity is still bigger than all real numbers. One half times infinity is still bigger than all real numbers. Negative ten times infinity is smaller than all real numbers. Negative one half is smaller than all real numbers.

 

True, but as infinity is a concept, and not an actual number, it cannot have such mathematical operations applied to it.

 

Your saying -∞ doesnt exist?

 

It exists as a concept, not an actual number.

 

How does a number that extends forever moved one place to the left not extend forever?

 

Say you move one number at a time. There is no point at which you can move the "last" number.

 

Well, .999 does not equal one because it is a repeating decimal. in that case in a math problem, you'd put a line over the 9 to show that the decimal repeats itself forever. Thats very basic.

-verry

 

The last number is at infinity so there is no last number just continuous numbers.