Does 0.999... Equal 1?

[steven787]

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.

@Bolded: exactly, .(3) or .33333333333333333333333333333333333333333... is a representation of of 1/3, it's a symbol for 1/3.  The digits .(3)... do not equal 1/3, the symbol .(3) represents 1/3.  The digits .(3) is approximately 1/3, it's the closest we can get in decimal form, but they are not equal.

Which is why those proofs don't mean anything.