When adding the positive integers taken to their own roots such as -1+2^(1/2)-3^(1/3)+4^(1/4) etc., in that alternating fashon, and I stop on the largest positive term, I get the value of the MRB constant. All of those terms except for the first one are irrational. However I previously mentioned that there is no proof that the MRB constant is irrational, but before I can prove anything I must know what I am proving.
In this post I would like to form a conjecture, and since I would like the conjecture to be true, I need to go to the edge of my reasoning as to which is more likely: Is the MRB constant rational or is it irrational? From this point on and until I have some convincing evidence, I am going to try to be neutral in my opinion as to its rationality.
I’ve been warned by experts that I might be working on this for a lifetime, without success..., and I don’t want to take their warning blithely, but I have no wish to stifle my curiosity. I do welcome your reasoning as well. Perhaps you can convince me of the ir/rationality of the MRB constant. I would dare go as far as to ask for unscientific opinions if that is all you have at this time, but if you have some reasoning about this issue I hereby beg for it!