0^0
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0^0
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Re: 0^0
#2This is ridiculous. Doesn't this seem counter-intuitive for it to be anything else besides 0 or undefined?
Re: 0^0
#3This is ridiculous. Doesn't this seem counter-intuitive for it to be anything else besides 0 or undefined?
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Re: 0^0
#4For the continuous use cases, it helps to look at a graph:
Re: 0^0
#5This is ridiculous. Doesn't this seem counter-intuitive for it to be anything else besides 0 or undefined?
Math and science are built upon many ideas that are both counter-intuitive and true.
Re: 0^0
#6This is ridiculous. Doesn't this seem counter-intuitive for it to be anything else besides 0 or undefined?
Please read the article before posting a question that is thoroughly explained.
Re: 0^0
#7That's a rather long text to say "it's an arbitrary -- and conveniently chosen -- definition of a special case of the power function similar to how 1 is not prime". I also think the presentation was chosen poorly: lots of wrong information before the correct approach is presented.
Wikipedia is probably a better source here: https://en.wikipedia.org/wiki/0%5E0#Zero_to_the_power_of_zer...
Re: 0^0
#8This is ridiculous. Doesn't this seem counter-intuitive for it to be anything else besides 0 or undefined?
If we don't have a specific mathematical context, then saying it's undefined is intuitive to me.
Without context, 0 is no more intuitive to me than 1. These two statements are equally intuitive to me, but they give different results for 0^0:
"Zero raised to any power is still just zero."
"Any number raised to the zeroth power is one."
Re: 0^0
#9This is ridiculous. Doesn't this seem counter-intuitive for it to be anything else besides 0 or undefined?
The article is making a very important point:
Even for things as "objective" as mathematics, definitions ultimately come down to what makes it convenient to manipulate symbols like an expert would.
This comes up all the time in fields as diverse as software engineering, law, finance, business, even hard sciences like physics - things are "right" because they're convenient, and because the consequences of them being that way make it possible to build on those results with new constructs, while doing it a different, more intuitive way would result in those constructs being impossible.
What the article is saying is that your intuition for it being 0 or undefined is because you've been exposed only to exponentiation as repeated multiplication or as the limit of some series; if you consider other theorems like the binomial theorem, and figure out what is necessary for them to hold without special casing, you'll decide otherwise.
Re: 0^0
#10Missing Q and A: But if mathematicians insist it is 1, why do high school teachers act like they know more than the mathematicians do?
A: They don't. The statement that mathematicians uniformly say it is 1 is simply false. My high school teacher had a PhD in math, I think it's fair to say she was a mathematician. And yes, she said it was undefined.