>>11517515so what, you imagine there are "infinite" 2's in 0.222-> ?
infinity is not a number. containing infinite 2's is indifferent from saying it contains unlimited 2's, which although is a reasonable assumption, is an assumption with definitions beyond it's scope.
there is no "infinite case". "infinity" is unreachable, unattainable, and would present issues even if it weren't. Such as, in this sum, if n=infinity, would provide , thereby making the rendered value something like in a similar way as , but that treats infinity as both reachable, incremented from the reals, as well as finite, an absolute end; which then begs the question of what is the largest real number before the +1 increment to ?
It also makes the math even more believable that 0.999... !=1 because it would instead be 0.999...0, allowing for a smallest real part to exist 0.000...1.
the only thing the dots imply is continuation.
if
2/9 > 0.2
2/9 > 0.22
2/9 > 0.222
and this is continued
>...then
2/9 > 0.222...
how long does it continue?
that's left up to the user to decide. It's not predetermined because there is no greatest number or greatest length in the scope of all things.
