Proof of 1 Not equal 0.999...

0*infinity=(0+0+0+0...)=0 (x+0=x x=0)
1=0.999... (agreed) 1-0.999...=0
(type 1) 1-0.999...=(1/10)*(1/10)*(1/10)... (from division by 10, 1-0.9 etc)
ab=0 if a or b=0; 1/10=0 ;10*1/10=10*0 ;1=0 ;x*1=x*0 ;x=0
(type 2) (1/10)*(1/10)*(1/10) ...=(1/10)^infinity=1/infinity=0
1/infinity=0 then 0*infinity=1 bu 0*infinity=0 ;1=0 ;x*1=x*0; x=0
Every number equals zero .(by 1=0.999...)

>>6
We're all talking about real numbers. If you want to take another system, be my guest. It's like arguing that 1 + 1 = 0 because it's true in the field with two elements.