/sci/ - Science & Math

Is [0,1] really uncountable? The proof seems to be fucking wrong for some lists. For example take the list
[eqn]0.900000 \ldots \\
0.080000 \ldots \\
0.008000 \ldots \\
0.000800 \ldots \\
\vdots
[/eqn]
then
[math]x = 0.988888 \ldots [/math] and
[math]x' = 0.899999 \ldots = 0.9 [/math] which is in the fucking list.