[quchen]

It's a flawed psychological argument though, because it hinges on accepting that 0.333...=1/3, for which the proof is the same as for 0.999...=1. People have less of a problem with 1/3 so they gloss over this - for some reason, nobody ever says "but there is always a ...3 missing to 1/3" or something.

[Scarblac]

The problem is that there are two different ways to write the same number in infinite decimals notation. (0.999... and 1.000...).

Thats what's counter intuitive to people, it's not an issue with 1/3. That has just one way to write it as decimals, 0.333...