|Syntactic Confectionery Delight|
Now you got me thinking. I have always been taught (as most of us have) that n^0 is 1. Now, why, do you suppose, that n multiplied by itself zero times, would it equal one? It isnt the same as n*0, I realize that, but if you think about n^1, you get n, right? meaning n^1=n. n^2=n*n, and n^0=? you dont have anything multiplied by anything else, so shouldnt this be undefined as well? I realize, also, that this has probably been defined by some dead mathematician who used this case to prove some wildy fantastic theorem, but still.
Am I totally off base with this?
my 2 cents about the 0^0 thing: 0^1 = 0 right? nothing multiplied by itself one time, should still equal nothing. so, if we were to think of this in terms of, oh, say, atoms, if you have no atoms muliplied by no atoms one time, you get no atoms (SURPRIZE!!!). now, if you have no atoms, multipled by no atoms, 0 times, you get 1 atom!
we just created matter!
call the pentagon!
note: energy to matter conversions do not apply in this simple example