|At 3 August 2013, 23:54:33 user rod wrote: [reply @ rod]|
I can't believe proclaimed educated mathematicians would fall into this ridiculous trickery and mathematical fallacy.
1-1 1-1 1-1... could only be either 0 or 1 depending on how many numbers(addends) you are willing to deal with. If you have an even number of negative and positive addends you would end up with a sum of zero, but if you have an odd number of addends you would end up with a sum of 1 if you started with 1( else -1 if you started with -1).
The only confusion in arriving at the correct answer is in the arbitrariness in how far "..." can go. Infinity is not a number but just an idea of unending continuity. If you want to introduce infinity in a calculation it has to be defined first with certainty, if not, you would end up with something that cannot be determined precicely.