A talk at the 6th Mathematical Transgressions meeting on the role of Arithmetic | N J Wildberger

[@peterrussell7846]

I enjoyed the talk and your answers to the questions. I particularly liked the different angle you gave on what you have been saying recently in your lecture on how a belief in infinite processes allow one to “prove” (not prove) famous open pure mathematics problems - when you described the idea of having two algorithms ostensibly for computing the same thing, the matter of how you prove they are the same algorithm, if you start with an algorithm and add in a twist which would prove an unsolved problem if true, then the difficulty of proving identity of the algorithms includes the difficulty of determine the truth of the unsolved difficult problem. Very interesting point and a nice way to demonstrate it.

[@UpCycleClub]

Thanks for sharing your talk.

[@repiv59]

I have followed you (NJW) since I came across your work of Rational Triginormy many years ago. It was put out in the video, the question, just what is a number? A very fundamental question and one that everyone will ask when first exposed to numbers and their uses. But when I think about that question, I do not have a concise answer, or know how to answer it concisely. I know of many analogies that I can use and remember but a clear, concise, and logically correct definition of a number (of anytype) I do not have or can recall ever hearing one. The closest I have come to logically sorting this out is with Zero and One only. Zero is the null / origin of reference for relationship with a number. One is the measure / value (in some given frame of reference) that sets the unit of all other numbers in their relationship to Zero. Other than this I can not come up with anything that is logically sound. When I think about the basic operations of arithmetic using the framework stated prior, I can understand division by Zero and One much more logically. When divide by one, you are dividing by what sets its value, and as such there is a singular and unique relationship between One and that number (the number itself). When you divide by Zero you are dividing by the reference for ALL the numbers, and as such there is no singular relationship or result, so it is undefined. I am no mathematician by any measure, but I do see the lack of solid logical underpinnings that are pointed out.