I’ve always wondered why anything to the zero power is 1 instead of 0.
Steven Shatz
1

Ah, it gets strange doesn’t it?! To introduce a little calculus thought without the calculus mumbo jumbo, let’s consider 2/x and see what happens as we divide 2 by smaller and smaller numbers approaching zero. What happens to our solution? Well, 2/2 = 1, 2/1 = 2, 2/0.1 = 20, 2/0.01 = 200… see what’s happening? Our solution is getting larger and larger the closer we get to dividing by zero. So I’ll offer you another option, perhaps division by zero results in infinity!

As a quick point of correction, 2 = x • 0 is undefined, not indeterminate. This is a confusing subtlety many students never learn. Undefined is sometimes substituted for the word “nonexistent” and perhaps that’s a clearer term. Point is, in our number system, there exists no solution for x in the equation 2 = x • 0 since we know anything multiplied by zero results in zero. Since that’s a false assumption we can’t substitute 2 = 0.

Indeterminate means there are multiple (perhaps infinite) solutions and there is no possible way of determining which is the most correct. As is the case in 0 = x • 0, here we see we could plug any real number in for x and the equation holds.

And YES, I hope this project takes us through Calculus and beyond! If people want to learn all that math, I am more than happy to write about it!

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