Can 1/3 and 1/3 = 2/6? It seemed so

Re:Can 1/3 and 1/3 = 2/6? It seemed so by ColinWright on Tuesday May 26, 2020 @09:59AM (#23311187)

> We conveniently ignore that this polynomial is defined at x=0 despite 0^0 not making any sense by ad-hoc defining 0^0 = 0 in this context.

What do you think the polynomial is? I ask, because in all situations similar to this that I've encountered it made sense to define 0^0 as 1, not as 0. If you genuinely have a case where 0^0 = 0 makes consistent sense then I'd be interested in understanding it.

So, what do you think the summation actually is when expanded?

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Re:Can 1/3 and 1/3 = 2/6? It seemed so by Spivak on Tuesday May 26, 2020 @10:58AM (#23311972)

Sorry you're right, it should be 0^0 = 1.

An example where 0^0 = 0 occurs when dealing with areas. The measure of the real line in the plane is zero but it's also a rectangle with sides (0, inf) and we define the area of a rectangle to be l*w.

You usually see this written as inf × 0 = 0 but you sometimes you see the interpretation as 1/0 × 0 = 0^0 = 0. And you know this is a an ad-hoc definition because you're not allowed to algebraically manipulate it at all.

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