Yeah, this is basically going to kill this, isn’t it. Oh well. Oops.
… yeah, if we’re going to use tiered values we might as well just explicitly make them program tiers, instead of bringing in a whole class’ worth of mathematical complication we don’t really need.
Well. Thanks! I can officially say I was less wrong than I was this morning.
Btw one thing worth noting if you really do want to work with surreals is that it may be more productive to think in terms of { stuff | stuff } rather than limits. (Similar to my “break ties by least birthday” suggestion.) Sequences don’t have limits in the surreals, but there is nonetheless a theory of surreal exponentiation based on {stuff | stuff}. Integration… well, it’s less obvious to me that integration based on limits should fail, but if it does, you could try to do it based on {stuff | stuff}. (The existing failed attempt at a theory of surreal integration takes that approach, though as I said above, that’s not really the same thing, as that’s for functions with the surreals as the domain.)
Arrgh.
Yeah, this is basically going to kill this, isn’t it. Oh well. Oops.
… yeah, if we’re going to use tiered values we might as well just explicitly make them program tiers, instead of bringing in a whole class’ worth of mathematical complication we don’t really need.
Well. Thanks! I can officially say I was less wrong than I was this morning.
Btw one thing worth noting if you really do want to work with surreals is that it may be more productive to think in terms of { stuff | stuff } rather than limits. (Similar to my “break ties by least birthday” suggestion.) Sequences don’t have limits in the surreals, but there is nonetheless a theory of surreal exponentiation based on {stuff | stuff}. Integration… well, it’s less obvious to me that integration based on limits should fail, but if it does, you could try to do it based on {stuff | stuff}. (The existing failed attempt at a theory of surreal integration takes that approach, though as I said above, that’s not really the same thing, as that’s for functions with the surreals as the domain.)