>>9397817

What is this convergance bullshit we aren't rounding this isnt fuckin 5th grade.

[math]0.\bar{9}[/math] doesn't converge to 1, it converges to even more 9's. The fact 9 is a maximal integer is completely regardless to the fact [math]\bar{N}[/math] is not related to [math]N[/math]

if [math]\sum_{n=2}^{\infty} 0.9 \stackrel{+}{=} \frac{9}{10^{n}} = 0.\bar{9}[/math]

then [math]\sum_{n=2}^{\infty} 0.1 \stackrel{-}{=} \frac{9}{10^{n}} = 0.\bar{0}1[/math]

We cleary have all the information we need from various proofs and tests and all we need to do is consolidate them instead of continuing to pretend [math]0.\bar{9} = 1[/math]

As much as infinity is actually an abstract concept that mathematicians pretend to fully understand, they should also understand that there are different number bases like hexidecimal and that [math]0.F _{16} = 0.9375_{10} > 0.9_{10}[/math] where that every step of

[math]\sum_{n=2}^{\infty} \big( 0.9_{10} \stackrel{+}{=} \frac{9}{10^{n}} \big) < \big( 0.F_{16} \stackrel{+}{=} \frac{F}{10^{n}} \big) [/math]

proves there are numbers greater than [math]0.\bar{9}[/math]

and dont be retarded with

>i-if you mark on a number line every 9th, you'll eventually run out of room and just mark 1.0

cause if you try to do the same with [math]0.\bar{1}[/math] you'll eventually make it to 2.0 of you're that retarded, or dumb enough to say [math]0.\bar{1} = 0.12[/math]

like damn, fuck. 9 is not a special number that gets to play by different rules than all the other numbers.