why does 0 to the power of 0 equal 1?
In: 97
I think the main confusion is thinking x^y means x times itself y times. This is a property of the exponential function when x and y are non zero positive integers, but using this as a definition quickly becomes nonsense. For example what does it mean to do 2^(-3)=1/8. Are we multiplying 2 negative 3 number of times? What does it mean to multiply negative times. Or how about 2^1.5, what does it mean to multiply it one and a half time? What is a “half” multiplication. Or 3^pi and dealing with irrationals, or with imaginary numbers, or as you mentioned things to the exponent 0. For this reason, the “actual” definition of exponents is different in mathematics and it just so happens we can prove this property holds with the “actual” equation for positive integers. The real equations are more confusing and need a deeper knowledge of math to understand, which is why schools simplify it with teaching a wrong definition that works in some cases and is more “intuitive”.
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