JeremyP's Blog

""Not a proof" so why the "QED"?" says Rich.

Well actually, it is not far off a proof as it happens. Consider the number 0.11111... (= 1/9). What does this mean? Well, 0.1111... is shorthand for

1/10 + 1/10² + 1/10³ + .... = 1/9

Clearly

9 . (1/10 + 1/10² + 1/10³ + ....) = 9/9

and therefore by the distributive law

9/10 + 9/10² + 9/10³ + .... = 9/9

or 0.999.... = 9/9.

QED

Well not quite. I have assumed

1/10 + 1/10² + 1/10³ + .... = 1/9

But that is trivially easy to show.