>>9728345Coming back to my original post and how both OP equalities abuse the vaguely, poorly defined implement of infinity to achieve their solutions, we will now prove it.
The common and incorrect proof for 0.999r = 1 is as follows
>x = 0.999...>10x = 9.999...>10x - x = 9>9x = 9>x = 1This relies on an abused concept called decimal shifting. Shifting is also used in ramanujan, we'll get to that. More to the point, calling it shifting is actualy sleight of hand misdirection.
In a normal number like 0.99, when we try
x = 0.99
10x = 9.9
what we actually did was shift the decimal over. There are still two promary 9 elements both before and after the shift multiplication.
in the failed solution for x= 0.999..., instead of actually shifting what is instead occurring is an extra 9 is being invented out of thin air, roughly equivalent to
>x = 0.99>10x = 9.99where there now exists one more primary 9 element that didn't exist before.
Aside from misdirection, it's also literally just shit retarded math. Its objectively incorrect.
0.99 × 10 is NOT EQUAL to 9.99
defacto
Where they had infinite 9's in x=0.999..., after 10x they suddenly have infinity+1 total 9 elements in the solution, instead of the trailing 9's after the decimal now properly having one less 9.
This literal same exact fucking retarded method is used by ramanujan in his proof of , where he assigns
>A: 1 + 2 + 3 + 4 + . . .>4A: 4 + 8 + 12 + 16 + . . .>faggoty "shifting">A : 1 + 2 + 3 + 4 + ...>4A:0 + 4 + 0 + 8 + 0 + ...>A-4A = 1 -2 + 3 - 4 + 5 - ...Which is already fucked up but he continues to do it in further steps. He presumes adding 0's doesn't change the self-contained sum, yet then defies this logic by misdirection to the fact he is comparing set element partial sums between the unaltered original set of sums 1+2+3+4+... to his arbitrarily altered mid-equation retard sum of 0+4+0+8+...
Same exact deceit occurs and is entirely disingenuous and wholly invalid
