A comic strip  (which you can see here after the jump) raised a mathematical conundrum that I’ve been trying to get my mind around.  Maybe you can help.

(1) 9 x 1/9 = 1.   Right?  That’s what the fraction 1/9 means.

(2)  1/9 = .1111111. . .  If you turn 1/9 into its decimal form, by dividing 9 into 1, the result is .1111111. . . [meaning a repetition into infinity]

(3)  9 x (.1111111. . .) = 1    Substitute the decimal form for  1/9 in equation (1).

(4)  .9999999. . . = 1      Do the calculation in equation (3).   9 x .111111. . .  is .999999. . ., another repetition into infinity.  The number by itself is short of 1, infinitely short, but you could go into infinity and it would never be 1.  AND YET, in the equation, .99999 in an infinite regress EQUALS 1.

How can that be?