**Background** I am not a professional mathematician. I am researching Surreal numbers & games for fun (I think they are truly beautiful). If this question is not appropriate here, I beg forgiveness & ask that it please be migrated it to MSE.

I read More Infinite Games by John H Conway recently & have not been able to stop thinking about the following line (page 4):

Note that $\uparrow$ is not a number: it is the value of a game, which is a more subtle concept. Also note that $\frac{1}{\uparrow}$ is not defined since it would be bigger than all surreal numbers and there are no such numbers. (In fact, it does exist but is one of the Oneiric numbers.)

Unfortnuately, the only thing on the internet about the Oneiric numbers is this paper. If my current understanding is correct, a part of the problem is that the reciprocal of games is not (yet) defined. As previously stated, I'm not an expert & have no clue if working out the reciprocals of games is an impossible (or just very difficult) task, or even if it has already been done.

It has been suggested by a couple people that I try to find someone who knew Conway & might have some idea of what he was thinking. I would be elated to do so. Alternatively, perhaps someone who is knowledgable about the Surreals might venture to take a crack at a definition.

Thanks for taking the time to read this question, I hope it isn't a waste of anyone's time.