Math Is Fun Forum

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Contradiction?

I argued with my father about the 0.9999...  question. It's , of course I believe it's equal to 1

 
I said 0.0000(infinty)1 is zero.
He said: consider this function 1/x (x>0). 1/x is not connect with x=0, you couldn't find the integration between [-1,1] directly, have to do it by parts, because its not continous, therefore it's not 0.
I said, the number isnt even a point on this function.  Infinity is not number, you can't substitute in to the function and get that value.
He said, well, what's the least distant between the points on this function and x=0 , it's zero. It's not continuous and now it's continuous .

I think his thinking is obviously flawed, but I couldnt spell it out lol,help

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Contradiction?

He said: consider this function 1/x (x>0). 1/x is not connect with x=0, you couldn't find the integration between [-1,1] directly, have to do it by parts, because its not continous, therefore it's not 0.

That has nothing to do with the question.  The question is for 0.00...1, which has to do with its value as you approach infinity, not 0.

He said, well, what's the least distant between the points on this function and x=0 , it's zero. It's not continuous and now it's continuous .

Yea, it goes to 0.  But there doesn't exist a single number such that f(x) = 0.  The part I highlighted in bold just doesn't make any sense whatsoever.

Typically, most people accept the 1/3 argument:

1/3 = 0.333...

Multiply both sides by 3 and you get:

1 = 0.999...

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Contradiction?

Ah, thats clears up a lots. Thanks