Do you understand that there is a difference between and ?
Now is a number between those two.
Well I just decided to refresh my math skills so started to reread an old Calculus book I have had for a while.
I came across an end of chapter problem that inquired whether
0.999999... < 1.0000000
It asked to represent 0.9999999... as a fraction of integers to arrive at an answer
So I did this
x = 0.9999999999
100 x = 99.9999999999
- x = - 0.9999999999
99x = 99
x = 1
The second part of the question referred to finding a real number between 0.9999999999 and 1.000000000
So I did this 1/2(0.9999999999+1)
=1/2(1.9999999999)
=0.9999999999
Why would I get 1 when I tried to represent 0.9999999999... ( is it a rational number with repeating digits) as a fraction of integers