Subject: Higher than infinity? Problem where infinity is too small....

I know I sound 3th gradish by asking is there a number higher than 
everything, but there is a problem which I can't solve. 
Mathematically, infinity can be defined as 1/0, right? Anyway, when you 
multiply 0 * 1/0, you get 0/0, which is any real number.
If infinity is everything, then shouldnt it be able to break free of 
normal bounds put on numbers? For example, 1^x is always 1.However, if we 
insert 1/0 as x, we get 1^1/0, which is also the 0 root of 1. (I am going 
to use @ to mean radical sign...)
0@1 = x
1   = x^0
This means x can be any number because any number ^ 0 is 1. However, when 
I did 0^1/0, here is what I got: (@ means radical sign:)
0^1/0 = x
0@0   = x
0     = x^0
0     = (x^1)/(x^1)
0     = x?
I am saying here that x^0 = (x^1)/(x^1), which is true, right? And since 
0/0 = 0, because 0 = 0*0, doesnt this mean that 0^(1/0) equals 0? What 
then, can break the "bounds" on 0 and put 0 to the power of a number is 1, 
or 2, or whatever... Infinity, I conclude, does not work in this case...

Would you need an number higher than infinity, in this case? I know it 
sounds meaningless, but would you...? Or is my basis that 0/0 wrong and 
0^0 is 0/0 wrong? Im not sure which....

Re: Higher than infinity? Problem where infinity is too small....