Does 0.999... Equal 1?

[HappySqurriel]

Rath said:

steven787 said:

HappySqurriel said:

 

It really isn't ...

On the left hand side of my equation I will deal with numbers using fractions, on the right hand side of my equation I will deal with numbers using decimals

1 = 1

1/3 = 0.333...

(1/3)*3 = (0.333...)*3

1 = 0.999...

 

 

 

Now, I see that you guys want to keep insisting that 1/3 = .333333.  it doesn't it's ~.

 

I would argue that 0.(3) is the decimal representation of 1/3 as it is infinitely long. Basically it's better to present a recurring number as a fraction as it's less ambigious but they are equivalent.

 

The truth is that fraction and decimal representation of numbers both have their flaws and that (most) mathematicians are very aware of that ... The problem (at the moment) is there are no other representations which are better