a = 0.999999.... {\displaystyle a=0.999999....} לכן 10 a = 9.99999999.... = 9 + a {\displaystyle 10a=9.99999999....=9+a} 10 a − a = ( 9 + a ) − a = 9 {\displaystyle 10a-a=(9+a)-a=9} לכן 10 a − a = 9 {\displaystyle 10a-a=9} , כלומר 9 a = 9 {\displaystyle 9a=9} כלומר a = 1 {\displaystyle a=1} .