I’m too dumb to get it
In: Mathematics
The whole “x^m / x^n” argument is a great way of showing that it must be so, but there is a much more relatable, “real-world” explanation for x^0 = 1. As such, the “no! It’s just because we defined it that way!” response is wrong – this time. It is true that that is sometimes the answer, but not here.
How about an ELI10? This operation (powers) describes the number of possible outcomes. So, if you were to flip a coin once, how many possible outcomes are there? Two – heads or tails, and 2^1 = 2. If you were to flip it 7 times, how many possible strings of heads and tails are there? 2^7. If you flip the coin 0 times, how many possible outcomes are there? Well…1, right? You get nothing. Thus, 2^0 = 1.
This of course ignore the interesting philosophical discussion of how to identify and count nothingness, but at a real-world level it is correct.
This understanding of exponentiation is of course restricted to non-negative integers in both the base and the exponent. By extension you then define the operation for all complex numbers in the base, and then you properly have the stated result. You can also extend to all complex numbers in the exponent. If you prefer to cut back down to real numbers, you of course get weird looking rules that come with that restriction.
Lastly, always remember – don’t drink and derive!
Latest Answers