Fun.
a choose b is defined as the number of ways to "choose" a elements from b. So this number is the same no matter what number system we are using. 5 choose 2 is still 10, even in this number system. Of course, that means we can't use the (n!)/( (n-k)! * (k!) ) formula anymore, since factorials don't work normally. We'll have to find something different and that will take a while...
Let's graph the function y=x+2! Of course, since our set of inputs for the function is our number plane, and our set of outputs is also a number plane, we would be graphing not on a plane, not in 3D space, but in hyperspace. This is the craziest thing I've ever seen. Since it's so crazy, I can't visualize it. So I'll stick to numbers with no leading zeros. Graphing y=x+2, we get this image:
They are all in a line! This makes sense, because after a bit of thinking, you'll come to realize that y=x+2 in base-potato corresponds to y=10x+2 in base-10. Well, unless you are working with leading zeros (4D graphing), becuase then 0+2=02. This makes me want to have two versions of base-potato. Simple base-potato, which does include numbers with leading zeros, and complex base-potato, which includes the entire potato plane. That would mean we're currently graphing in simple base-potato. Except, wait a minute. What happens if I add decimals into our inputs? If I add tenths places, another line is formed. That is.. REALLY WEIRD.
This phenomenon occurs because, of course, 1.1+2=1.12
What about x-values with hundreths places? It seems that we get yet another line, that is basically the same as the x-values-with-tenths-places line, but shifted downward.
Part 6 coming soon. Soon. I promise. Make sure to check back to my website soon. I probably need a mailing list, but I'm not sure how to code that. Email potatocubers@gmail.com if you have questions or want to add something to this.