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# how can infinity be pointless?

schumway
saw the discussion re .9999 =1 and found it funny that the conversation was closed with the comment that it is a pointless conversation YET it is covered in many university papers and debates.

course I also find it funny that they usually mix notations so they get caught in rounding errors. Had the same discussion with my brother-in-law and he was just as lost with 2 degrees and one masters and still in school.

the problem with the
3 x 1/3 = 1 so
3 x .3333 = 1
.9999 = 1

is that .3333 is rounded off. So there is an error in the calculation. Then it becomes a point of what is acceptable amount of accuracy. Is 6 sigma accuracy good enough? Is 2 decimal places (ie currency) good enough when our interest rate is calculated at 2% per year calculated... um.. daily (ie 2/365 or 0.0054794520547945205479452054794521% per day)

same thing happens with .9999 = 1
.9999 is not the same as .9 "repeating" because it isnt repeating anymore... so somewhere along the line you have stopped writing down the 9's. It is rounded up by calculators because they can not maintain the accuracy nor notation.

you can also tell that by

.3 repeating + .3 repeating + .3 repeating

.33333
.33333
.33333
.99999

as you add down the columns for the .3's they equal .9... and it would do this all the way to infinity... um.. and beyond (trademark)
this is quite old. hundreds of years old

http://en.wikipedia.org/wiki/0.999...
Afaceinthematrix
I've always proved that .9 repeating = 1 like this:

x = .9999....
10x = 9.999... // multiplying each side by 10
10x = 9 + x // 9 + x is the same as 9.999...
9x = 9 // subtract 9 from each side
x = 1 // solve for x