/sci/ - Science & Math

>>9321545
Lets take your example and apply ㅌ to it
0.999...=x+ㅌ
9.999...=10x +10ㅌ
10x-x +(10ㅌ-ㅌ) =9.999...-0.999...
9x+9ㅌ=9
x+ㅌ=1
0.999...+ㅌ=1

Where your original problem makes a fault is here at
>10x-x=9.999...-0.999...
>9x=9
>x=1
>0.999...=1

x = 0.999[9
10x = 9.999[9
But 10x-x, 9x, does not equal 9.0
9x = 8.999[1

Your problem derives from seeing the decimal as seperate from the whole, so you see 0.9, subtract that from 9.9, and get 9.

if it were seperate from the whole, you would consider x+x = 1.999[9, but that is only true if one and only one of those x values is equal to the whole number 1, otherwise it is
0.999[9
+0.999[9
_____________
1.999[8

if one x is presupposed to equal 1 while the other x is presupposed to equal 0.999[9, that just doesnt work. If x=1, then the answer is 2, not 1.999[9. if x=0.999[9, then the answer is 1.999[8