0.9999.... = 1.0

[Zkuq]

dsgrue3 said:

Jay520 said:

We're not solving that x = 0.999. We are showing 1 = 0.999..

...and that is not a valid way of showing it.

What if we forget x and simply write:

    9.999... = 10*0.999... (I believe we can agree on this.)

    9 = 9*0.999... (subtract 0.999...)

    1 = 0.999... (divide by 9)

All right here, right? Well then, let's make writing the thing easier and say x = 0.999... The exact same process written in terms of x:

    9.999... = 10*0.999... = 10x

    9 = 9x (subtract 0.999...)

    1 = x (divide by 9)

Now do you claim that when I decide I want to write the equations in a more convenient form using symbols, the whole thing loses validity?