@0celo7 yup. Behind closed doors, your supervisor can't go, and you can't discuss your thesis with either examiner before the examination. Rather different to other places.
Apparently there are several sets of generalized numbers
But $\mathcal K_e$ is ALSO not a field
Dang it
I guess I won't be revolutionizing QFT this week
there seems to be a paper about a field of generalized numbers, but I don't know if those are at all related to generalized functions
Generalized numbers have this weird thing where there's several things that are "zeros"
You have negligible numbers and strictly zero numbers and shit
"We present a differential algebra of generalized functions over a field of generalized scalars by means of several axioms in terms of general algebra and topology"
"In our approach the set of scalars (the constant functions) of our algebra of generalized functions forms an algebraically closed Cantor complete field, not a ring with zero divisors as in the original Colombeau theory"
The following are not the point of science: 1. Sounding dramatic. 2. Intentionally making something sound confusing and then explaining it in a new, but unnecessarily convoluted way.
This may sound trivial, and you may think I am joking.
I am not. This is important and I hope to the heavens and the powers of the universe that everyone here will remember this when they review a paper that delivers new information matter-of-factly.
We see papers for review all the time which essentially say "You might think quantum systems are actually classical. If so, you would analyze it like this. In this work, we do an experiment and show that the classical thinking doesn't work by analyzing the data in a new way".
We also get papers rejected for being not exciting enough (literally got that on a referee report) despite the fact that the paper delivers a solution to a decade-old and very important problem.
IN other words, we didn't sex it up enough, so they rejected it.
Hilariously, both referees said the paper was very clear, and then the second referee rejected the paper for being "too obvious".
That's like reading a really good math proof and saying "don't publish this in a book because it makes the theorem too obvious".
"Our set-theoretical framework is the usual ZFC axioms in set theory with the axiom $2^{\mathfrak c} = \mathfrak{c}^+$, where $\mathfrak{c} = \text{card}(\Bbb R)$"
@ACuriousMind A world famous leader of quantum information publicly declared the problem as "the skeleton in the closet of our field". I solved this problem, and the referee says it's too obvious.
@ACuriousMind My plan is basically to go around the community and loudly voice my opinion that we need to value clear useful results more and dramatic bullshit less.
1. Application of quantum computing to new problems, such as molecular simulation, physics model simulation (i.e. running an digital simulation of a Bose-Hubbard model)
2. Doing pathetically simple experiments and showing that a new flavor of analysis predicts the outcome. This typically comes with statements like "You might have though classical mechanics would work here, but surprise! it doesn't as shown by our new flavor of quantum analysis".
No, we are playing "I should not have taken a 5 day break from reading this highly technical manuscript because I am now confused beyond all hope of recovery"
I am fairly sure that quoted thing is wrong.
it should be "all bump $n$-forms with unit integral"
"For every infinite cardinal there is unique, up to isomorphism, non-standard extension $^* \Bbb R$ of $\Bbb R$ such that $\text{card}(^*\Bbb R) = \kappa^+$"
Hm
I wonder if that means that this set of generalized numbers is isomorphic to the hyperreals
