Here's one stupid, simple proof that doesn't require any predefinition. We do longhand division of 9 by 9, but start by putting a 0 in the first place.

Here's one stupid, simple proof that doesn't require any predefinition. We do longhand division of 9 by 9, but start by putting a 0 in the first place. 0.99 9 | 9.0000 0 9 0 8 1 90 Hence, 9 / 9 = 0.999 = 1.