The question whether surreal or hyperreal numbers (that both contain the reals, even if they have the same cardinality) could be useful to provide a more satisfactory theory of QM is maybe more interesting. -yuggib
I have been pondering this question for a while now, but was not able to formulate it so succinctly until I saw the above quote.
I still don't feel able to properly convey my intuition around why this is a good approach..
is not zero, but neither positive nor negative, and is therefore said to be fuzzy and confused with (a fourth alternative that means neither "less than", "equal to", nor "greater than") 0
is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1
—usually taken to have the value “0” and “1”, like a bit. However, whereas the state of a bit can only be either 0 or 1, the general state of a qubit according to quantum mechanics can be a superposition of both.
"It is likely to be a fresh research question, and you the person one most interested in the entire world in finding an answer --- in which case it is most probably up to you (and your opportunity!) to obtain the answer first." -Niel
While the motivation to wanting to make this work may not be apparent at first, a big piece of what I'm wanting to accomplish is creating a quantum algorithm based on surreal constructions for a quantum intelligence that can use game theory for computation.
How can surreal maths be used in quantum computing?