0.999... = 1

Today I was reading some forum where engineers and mathematicians fighting over an equation

0.999... = 1


Engineers say that is wrong.0.999... is only approximately equal to 1. Mathematicians say it is exactly equal to 1.
Before I judge who is correct let me see whether I am an engineer or a mathematician.Hmmm. Tough question ?Not really, I can easily decide on mathematicians side because I definately know that I am not an engineer.Though my degree says I am an Aerospace Engineer ,I haven't learnt or remembered about anything which I learnt regarding engineering or aerospace.Even if you disagree I am gonna settle with mathematics.

Coming to the equation, Eng's argument is that we cannot really approximate and say it is equal and they argue that by saying 0.999...=1 we are rounding off.Mathematicians argue that 0.999... with 3 dots at the end implies that the 9 is a repeating decimal infinitely.So it is equal to 1.

Actually, we can prove this.

lets say x=0.999....
10x = 9.999...
---------
10x - x = 9.000....
that means 9x = 9 => x=1
Hence proved :)

There are other solutions also but I like this one.