why does 0 to the power of 0 equal 1?
In: 97
It isn’t equal to 1. It is undefined. That is, it isn’t well-defined as a number (having a set address on the number line.)
One good way to see this is to complete the following sequences:
81, 27, 9, 3, __;
16, 8, 4, 2, __;
1, 1, 1, 1, __;
0, 0, 0, 0, __;
It should be obvious that the answers are 1, 1, 1, and 0.
Now I’ll write the exact same sequences in a different format. (Remember that ^ means “raised to the power of.”)
3^4, 3^3, 3^2, 3^1, ___;
2^4, 2^3, 2^2, 2^1, ___;
1^4, 1^3, 1^2, 1^1, ___;
0^4, 0^3, 0^2, 0^1, ___;
Now the answers are obviously 3^0, 2^0, 1^0, and 0^0. The first three examples seem to suggest that “any number raised to the 0 power equals 1.” But the fourth example suggests that “0 to any power equals 0.” Since a number cannot be both 1 and 0 simultaneously (quantum superposition aside), 0^0 is not a defined number.
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