Quote:
Originally Posted by Tolnaftate2004
I can rearrange the numbers to do division first... If they're both multiplied by 0, I'd say the statement reads 0=0 and leave it at that. There is no infinity in either case. On top of that, 0/0 could be anything in C. Also, the taylor series for e (and sin and cos probably, along with others, I really haven't thought about it) needs 0/0 to be 1 to work. Oh, and TI-89s replace 0/0 with 1... ???  |
The TI-89 is wrong. The only way you can describe 0/0 equating to one is because of the algebraic rule that a/a is always equal to one, but that implies that a is a nonzero number. If you think about what division means in algebra, it establishs a ratio. if you did 2/5, then you would have ,4:1, if you did 1/2, then you would have .5:1, if you did 5/2, then you would have 2.5:1, etc etc. but what if you have a/0? You could never establish it as b:1. a/a as a ratio is 1:1, unless it is 0, which is why a/a when a=0 does not equal 1. The TI-89 incorrectly uses an algebraic rule in a situation where it cannot apply.
The only way to solve 0/0 is to use a limit approach, which makes it equal to 0, and which is the right answer defined by modern mathematics .