0.99999999.......

[Citizen James]

Libertas pretty much nailed it, but I want to give a slightly more formal argument.

1/3 = .3333333333....

multiplying both sides by 3 we get

3(1/3) = 3(.3333333333....)

3/3 = .9999999999999999

Noting that 3/3 is equal to 1 we have:

1 = .9999999999999999...  QED.

Floating point computation is a whole other ball of wax because computers can only hold a finite number of places.    The number given is not the exact answer, but a (hopefully) good approximation of it.

[Citizen James]

Question for the math and number geeks out there.

Could 1 - .9999(repeating) = *, be regarded as true?
* defined as an infinitesimal

If you really want to get your geek on, Wikipedia has a quite well documented page on the subject.

I suspect part of the confusion is in comprehending the concept of infinity.  And that it is a  concept - not a number.  A phrase such as (infinity plus one) has no real meaning beyond humor value.

The Zeno's paradox mentioned earlier gets to the heart of the concept.  Consider the following situation - a runner is heading toward the finish line.   In a certain amount of time, he will be 9/10ths of the way there (.9), later he will close 9/10 of the remaining distance (reaching .99) this continues for another 9/10ths of the remaining distance (.999) and so on.  Will the runner ever cross the finish line? (try this yourself if you aren't sure).  Infinitely close (and infinitesimal distance) is nothing.  The great and mighty wiki also has an article on the concept of infinitesimal (as well as noting that the concept is different than the common usage - merely meaning 'very small').