Quote:
Originally Posted by debussybunny563
I'm interested in your opinion...
Do you think 0.999.... is equal to 1?

I think the point here is that the "..."'s represent a iteration of the digit "9" indefinitely. Therefore you meant .999999999 with an infinite number of 9's afterward, right? So using the algebra I know to convert repeating decimals into fractions:
x = 0.999... //Set x to the decimal:
10x = 9.999... //Multiply by ten on both sides.
10x  x = 9.999...  0.999... //Used the information above for this
expression
9x = 9 //Simplify (since the repeating decimal part is
the same for both 9.999... and 0.999..., they
cancel out)
x = 1 //Divide by nine on both sides.
Therefore 0.999... is equal to 1.