2011-03-14, 01:45 PM
Well.
3 times 0 translates into: I have ZERO number three, how much does that ADD up? 0 + non-existent 3 = 0
3 to the zero power translates into: I have ZERO number three, how much does that multiply into? 1 x non-existent 3 = 1
The non-existent 3 is just... not there, it doesn't modify the 0 and 1 (or any variable x) in any way.
x^0 = 1 is just that. x^0 is non-existent and unable to affect other components multiplied by it.
The representation of "something that doesn't change anything when multiplied by" is, conveniently, existent, and it is 1.
3 times 0 translates into: I have ZERO number three, how much does that ADD up? 0 + non-existent 3 = 0
3 to the zero power translates into: I have ZERO number three, how much does that multiply into? 1 x non-existent 3 = 1
The non-existent 3 is just... not there, it doesn't modify the 0 and 1 (or any variable x) in any way.
x^0 = 1 is just that. x^0 is non-existent and unable to affect other components multiplied by it.
The representation of "something that doesn't change anything when multiplied by" is, conveniently, existent, and it is 1.