>>16813190
>0.999... (base 9) = 1.111...
You cant have a symbol in your number same as the base :
Base 10 :
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9] the symbol "10" doesn't exist.
Base 9 :
[0, 1, 2, 3, 4, 5, 6, 7, 8] the symbol "9" doesn't exist.
...
...
Base 2 :
[0, 1] all the symbols above 1 dont exist.
>0.999... (base 9)
Nope, syntax error in math.
1 (base 2) = 1 (base 10) = 1 (any base)
10 (base 2) = 1*2^2 + 0*2^0 (base 10) = 2 (base 10)
0.1 (base 2) = 0*2^0 + 1*2^(-1) (base 10) = 1/2 (base 10)
0.01 (base 2) = 0*2^0 + 0*2^(-1) + 1*2^(-2) (base 10) = 1/4 (base 10)
...
You double in a direction, halve in the other.
For others bases, you base in a direction and debase in the other.
Also 10*0.1 or 100*0.01 or whatever, in any base is always 1 :
10(base 2) * 0.1 (base 2) = 2 (base 10) * 1/2 (base 10) = 1
10 (base 10) * 0.1 (base 10) = 1
A video from great mathematicians here :
https://www.youtube.com/watch?v=PPBsUo4A8fg
