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...)

>>64
Tell me, do the sequences {1/2, 3/4, 7/8, 15/16, ... } and {2/3, 8/9, 26/27, ... } approach the same value? If so, why do you think that the sequences {0.9, 0.99, 0.999, ... } and {1.0, 1.00, 1.000, ...} do not? The article you linked specifically states that a number is equal to an infinite sum of the form Sum[i=0,+inf](a_i/10^i). And, ironically, it specifically links the article about proving 0.999... = 1!