Invalid/undefined operations.
The real problem is that you are doing illegal, immoral, and fattening mathematical operations.
In most contexts, operations which cannot be defined in some finite fashion are either not defined or not allowed.
The infinite series you are using does not converge. Its sum is undefined.
In general, any process which requires an infinite number of operations is undefined, illegal, invalid, immoral, whatever.
Convergent series (for example) are defined in a manner which avoids a requirement for an infinite number of operations to determine the limit and/or apply the definition.
You gave a reason for undefined.
Simonm: You gave four plausible values for the sum of that series.
While I do not like the average much, it is not unreasonable. BTW: I always saw this series presented as 1 -1 + 1 -1. . . which has an average of 1/2.
I object to saying 1 and 2 simultaneously, but either value looks reasonable by itself.
What you have done is present a wonderful argument for saying that the sum is undefined. Id est: It is impossible to decide which of several possible values is correct. That situation is one meaning of undefined.
Hate to break up the party but?
Why in the world would u need this?
Many values simultaneously
What about the case of 0/0 ?
Considering a line:
y = mx + b
we can say that m = (y-y0)/(x-x0).
Let y0 = 0 and x0 = 0
when x=2 and y=2, m = 1
But when x=0 and y=0? It stays 0/0
However:
1. anynumber / 0 = infinite
2. m is constant
So, as the constant value is 1, 0/0 = 1 in this case.
But the line could have a diferent value for m and 0/0 would have a diferent value.
I suppose it is correct to say that infinite can be different values... or simply undefined. :rolleyes:
Correct me if I'm wrong or if I'm being immoral and unethical. :D