07/18/2019, 02:09 PM

Hello! I'm a 21 year old amateur mathematician who was homeschooled until the age of 16 and has never set foot in a public school or college (yet)... everything I know about math I either learned from my father (an electrical engineer) or from my own studies. I'm a hyper-creative type so it's hard for me to hold myself to studying one specific subfield thoroughly and getting grounded in the basics - instead I keep coming up with crazy ideas and trying to figure out how to make them work (and usually getting told all my ideas are useless / meaningless / incomprehensible by "real" mathematicians on reddit...)

I discovered this forum while looking for information on fractional hyperoperations, and then discovering zeration and the "controversy" so to speak around it - I am now studying hyperoperations a bit to try to see what would be required to axiomatically derive properties of different variants of zeration and the higher operations. I have some extremely vague suspicions about how this will turn out but nothing consequential yet. (And yes, I've read all the threads I can find on the subject here, but probably should read them again multiple times!)

Besides that, other things I've played with, which are less relevant to this forum, are: a mixed-radix number system with place values in Sylvester's sequence (minus one) whose digits are entire numbers of one fewer digit, and which thus has a tree, rather than linear, structure... *another* number system based on golden ratio base but with the only legal digits being 1 and -1 (so that zero is an infinite sequence of 1,-1,-1)... a logic of directed multigraphs whose arrows can sort of "travel along" one another to make inferences, which has interesting similarities to Linear Logic... etc.

Basically I'm prone to inventing weird stuff and not knowing how to actually prove anything about it

Anyway I look forward to getting to know you all and maybe you'll be able to help me learn more about Tetration and the other hyper-operations (and your attempts to make Zeration and fractional ops work) - I don't know any analysis yet except the vague general ideas of differential and integral calculus, so I can't really follow a lot of theorizing about tetration yet :3 but I hope to learn.

I discovered this forum while looking for information on fractional hyperoperations, and then discovering zeration and the "controversy" so to speak around it - I am now studying hyperoperations a bit to try to see what would be required to axiomatically derive properties of different variants of zeration and the higher operations. I have some extremely vague suspicions about how this will turn out but nothing consequential yet. (And yes, I've read all the threads I can find on the subject here, but probably should read them again multiple times!)

Besides that, other things I've played with, which are less relevant to this forum, are: a mixed-radix number system with place values in Sylvester's sequence (minus one) whose digits are entire numbers of one fewer digit, and which thus has a tree, rather than linear, structure... *another* number system based on golden ratio base but with the only legal digits being 1 and -1 (so that zero is an infinite sequence of 1,-1,-1)... a logic of directed multigraphs whose arrows can sort of "travel along" one another to make inferences, which has interesting similarities to Linear Logic... etc.

Basically I'm prone to inventing weird stuff and not knowing how to actually prove anything about it

Anyway I look forward to getting to know you all and maybe you'll be able to help me learn more about Tetration and the other hyper-operations (and your attempts to make Zeration and fractional ops work) - I don't know any analysis yet except the vague general ideas of differential and integral calculus, so I can't really follow a lot of theorizing about tetration yet :3 but I hope to learn.