21–30 of 256 posts
I see this all the time with AI/machine learning. Most algorithms are based on assumptions that make the math work out better rather than being aligned with some "fundamental truth." The world is not linear, but it's much easier to approach it as if it were!
That'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...
In no way was wikipedia better, it was confusing and basically incomprehensible unless you already understood the material. His presentation was much better because it leads you to the answer instead of dropping it on you from the sky. (The difference between learning by rote vs learning by understanding.)
0 ^ any negative power = 1/0 = undefined = +- inf
So strictly only the right limit as n --> 0 of 0^n = 0. Not the limit.
I understand the "math"...the numbers...the work on paper. But how does that translate to something useful in the real world? That, after all, is what useful math helps us do...solve problems for the real, tangible world. Saying that 0^0 = 1 is a cool math game; but translate 0 into something in the real world (i.e. nothing, none, etc.)...and trying to make something out of it other than 0 or "indeterminate" starts t…
I think this is a by-product of the way we are taught maths at the very start; that it must somehow relate to real things. We start our understanding of maths by using real world objects like apples and we show how addition works and subtraction. I think perhaps it sticks in our head that everything must somehow relate to real objects and the real world.
We somehow get past that when we are introduced to things like square roots and integrals and higher mathematical concepts, but even with those we often try and relate them back to the real world.
I wonder of there are other ways to start teaching maths that doesn't start by using balls or apples? How would that work?
Another good reminder on how math itself is arbitrary and made up by humans (often for what's simplest/easiest), and not handed down to us by God. Luckily it's an extremely useful and extendable made up system. I see this all the time with AI/machine learning. Most algorithms are based on assumptions that make the math work out better rather than being aligned with some "fundamental truth." The world is not linear, b…
I understand the "math"...the numbers...the work on paper. But how does that translate to something useful in the real world? That, after all, is what useful math helps us do...solve problems for the real, tangible world. Saying that 0^0 = 1 is a cool math game; but translate 0 into something in the real world (i.e. nothing, none, etc.)...and trying to make something out of it other than 0 or "indeterminate" starts t…
http://arxiv.org/pdf/math/9205211v1.pdf
See page 6.
Another good reminder on how math itself is arbitrary and made up by humans (often for what's simplest/easiest), and not handed down to us by God. Luckily it's an extremely useful and extendable made up system. I see this all the time with AI/machine learning. Most algorithms are based on assumptions that make the math work out better rather than being aligned with some "fundamental truth." The world is not linear, b…