Basic algerbra.   ( a + b ) / 2  is a number that comes between two numbers.

    ( 0.9999~  + 1 ) / 2

1 / 3 = .3333~

.3333~ = .3333~

They are equal.

that isn't a number though, you just listed both numbers and then wrote "over two".

It's a formula to represent the number.  Just because it can be represented, doesn't mean the numbers are or are not equal.  It just means you need a better test to determine that.

OK, I'll go one step further. I'll personally paypal $20 to the first person who can name a specific number (not an algebraic equation) that is greater than 0.99999~ and yet less than 1. Th algebreic formula of (a + b) / 2 will not come up with a number between a and b if a = b.

 Note...and I was implying this...a real number between the two is required.  In other words, something to prove that the two are not equal.

*agrees with OP* jlauro - The over 2 thing is also the same number! *gasp* Alex - this math might be a little over your head. :P Write down the original question on your next math test and watch your teacher's head explode hehe.

2i (the imaginary number)

 2 is obviosly greater than 1, and yet if square i, it is a negative number so it's obviosly less then 1 and greater than one at the same time.

Good enough for my $20?   ;) 

 I know...  never said it wasn't    ;)

I don't feel like thinking so I'm gonna use regular math. 9 cannot go into 10 evenly 99 cannot go into 100 evenly 999 cannot go into 1000 evenly and it goes on and on, 999.... cannot go into 100... evenly Also another thing, 1/3x3=1, but 0.33333... X3= 0.999999... I don't care if I'm right or wrong, i just feel like not thinking.

 Close, but the answer is both correct and incorrect at the same time, no?