A more concise and intuitive demonstration that 0.9999...=1

[halfeye]

Most of the explanations I've seen of why 0.999...repeating equals 1.0 have seemed a little esoteric, but I just thought of a really simple demonstration showing that they're equal

Start with the number 1.1111....repeating
Subtract 1 (leaving you with 0.1111...repeating)
add 0.9999....repeating

and you see immediately that it gives you back the original number

Esoteric?

0.333.... = 1/3.

3 x 1/3 = 1, so 3 x 0.333.... = 1, so 0.999.... = 1.

What's esoteric about that?

It's worse than that, it's wrong Jim.

0.1111 + 0.9999 = 1.1111. Which may be what was meant by "the original number", but it wasn't immediately clear to me that that was what was meant.