i just realized i get really pissed when people believe in already-proven-false math things.
like how 0.9 repeating =1
its wrong, and when they continuously say it isnt, i for some reason get really pissed....
and here's my proof for all the people who disagree with me:
If 0.9 repeating DOES equal 1 let these mathematical truths first be in place to test it:
That 10 - 09 = 01
That 1.0 - 0.9 = 0.1
That 1.00 - 0.99 = 0.01, 1.000 - 0.999 = 0.001, etc.
And that 1.0...0 = 1
If we rename the number 1 as constant A, the 0.9 chain as variable B and the 0.01 chain as variable C
:. If you continue the process of adding a zero after the decimal in A, a 9 between the decimal and the pre-existing 9 in B and a 0 between the decimal and the pre-existing 1. And since no matter how many 0s are added after a decimal where there is no other number, the number remains the same, the equation 1.000000000 - 0.999999999 = 0.000000001, etc., would have the rule for every n number of 9s after the decimal, if this number is subtracted from 1, the difference will be n-1 number of 0s after the decimal, with a 1 at the end.
:. If you continue this insertion of numbers N number of times, it can eventually be rewritten as 1 - 0.9 repeating = 0.0repeating1 due to the fact that infinity can be finite, just so large that it is impossible to record.
For example, if this process continues for 10^100 times, the equation ends up being 1.00... etc with 100 zeros after it, subtracted by 0.9999...9 with 100 9's after the decimal, the answer should be 0.00001 with 99 0s after the decimal and a 1 at the end.
At no point in the infinite distance should these truths break down otherwise they are not considered truths.
And since in a base 9 system, 1/3 of 1 equals 0.3, and in base 12 it is 0.4: all base systems that do not have a factor of 3 therefore contain a repeating decimal and are thus not exact.
As well, given the equation Lim x-->1 from the negative side, the maximum value of x must be infinitely smaller than 1 but not 1, and given the truth that the 10 is the next number after 9, 0.9repeating is the number before 1 since adding another 0.0repeating1 would cause the carryover to become 1.
Therefore, it is correct to state that 0.9 repeating does not equal 1.