If you think about it, what is an irrational power?
Forgetting about complex numbers for the moment, even just taking something to the power of root 2 doesn't make sense.
Integer powers make sense, because x^n just means that you multiply x by itself x times. Fine.
Rational powers are fine as well, because for x^(m/n), you just multiply x by itself m times and then take the nth root of the result.
But when the power becomes irrational, there's no way to calculate the result (or at least, there shouldn't be). And yet these numbers exist. What are they?
That is the main reason. My calculator (mathematica 5) gives me -0.709608865301661-2.56893918954912i. I don't agree with that, because number is only real, or imaginary. And I asked this question, because I want to understand why is imaginary, because I dont know the divisor N, so I don't know wheter is odd or even.
Perpettum Mobile is b*lls*t (excuse me). There are some theories that explain how to gain matter from the vacuum, but I can't understand nothing at tis point. In my opinion the future major energy source is the hydrogenium fusion by reactors like TOKAMAK http://en.wikipedia.org/wiki/Tokamak . But current TOKAMAKs can't produce enought energy to self sustain reaction but one day this will be reality !!!
I just think that:
0,9999(9) = 1 - 1/infinity
1. So, in physics or chemistry we will think like this -> 0,99999(9) = 1
But mathematicians won't be satisfied, and I think this is the number that ends the (-infinity;1) .
2. but if we consider about limits:
1/infinity = 0 => 0,9999(9) = 1-0=1
3. And, at last there is algoritm to find the proper fraction:
0,9999(9) = 0,9 + 0,09 + 0,009 ....
x= 0,9 + x/10 |.10
I assume that x= 0,9999(9) is equal to x=1 at every equation, exept some cases like this
x=1 => 0/0=?
x=0,9999(9) => 0/x=0