Tuesday, October 30, 2007

Logically ... true!

Have you thought before how much is the sum of zeros "n" times?
"0" isn't it?
What about adding another big number of zeros?
Still the answer "0"?

Now what is the sum of adding zero uncountable number of times? Up to now nobody knows! A friend [Ahmed Sayed] told me that he can proof that adding zero infinitely number of times in a countable set is an undetermined quantity and here is his proof:

Let I be an infinite countable set;
SUM[i in I] (0) = 0 . SUM[i in I] (1)
But sum of 1 infinite times = infinite
Thus SUM[i in I] (0) = 0 . infinite which is undetermined quantity!

This is for countable set, what about uncountable set?

Why we haven't defined "0 . infinite" by 0 since 0 multiplied by anything make it zero..?
You cannot take one of infinities as 1 over zero because 1 over zero is undetermined quantity too and we say it tends to infinity only when the 0 is given by a limit!

This is math, sometimes crazy, but logically TRUE!