0.9999.... = 1.0

[walsufnir]

pezus said:

MDMAlliance said:

Talal said:

Not to sound arrogant, but it's a pretty established fact that 0.999.. equals 1.

I think we're using the word "fact" wrong if it is contested.  In pretty much any math equation you will ever come by, it will equal 1.  However, it is not a fact that .999... itself is actually 1.  Every time I see someone trying to prove it, it keeps showing me that they are either using circular logic, or are approximating, then claiming they are the same thing.

It is a fact and can be easily proven in many ways. One of the ways was in the OP last I checked.

x = 0.999...
10x = 9.999...
10x-x = 9.999...-0.999...
9x = 9
x = 1

And therefore: 0.999... = 1

I call this invalid as you can't really subtract infinite nu,bers from another. If you subtract it has to be a finite number.