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sniffnoyI mean, if cardinals are red, I guess ordinals can be blue, right?
Blue Kirby: Someone thought to buy Smash 64 for the Virtual Console for the house's Wii. I think Dan was a bit surprised I was so good at it. :D I realize I'm not by the standards of old Tufts House - I haven't played in quite a while, I keep failing to smash, I never learned to Z-cancel - but I'm certainly good against the people here. Much better than at Brawl, that's for certain. Need to play more, remember more. Took me a bit to remember how to play Falcon.
Obvious-but-funny-anyway-observation: The controls have been modified to match those of Melee. Hence Z-cancelling would now be done with the L button. I don't expect anyone to start referring to it as "L-cancelling", though.
Blue Water Fangs: I was down at GYGO and saw they had the Xbox version of Metal Slug 3 for cheap, so I picked that up. Hooray, Metal Slug 3 with a non-ridiculous number of continues. Heh - this TVTropes page refers to the Xbox version as a "porting disaster" because of this. Bah! If you can't beat a level in five lives, you aren't beating it properly, I say!
Well-ordering: Let's talk about integer complexity. I finally finished classifying n with d(n)≤21d(2), which means I can classify n with D(n)≤1, and... it's terrible. I decided to not even go through and finish it; it may be easy, but it's still not worth it. {n: D(n)=0} has a nice form, so I guess that's worth noting, but {n: D(n)≤1} really doesn't, so... why bother? (OK, I guess I can't say this for *certain* as I didn't finish, but it seems pretty clear.) Well, at least the statement that D(3n)=1 ⇒ D(n)=1 is kind of nice.
But! Stopping work on that means I can actually get back to work on interesting stuff. A few days ago I had the idea to, y'know, actually formalize the notion of certain types of infinite families of integers we'd been using implicitly the whole damn time, and, well it's been very helpful. For instance, we've been able to finally prove that the set of defects is well-ordered! (It has order type ωω.) I was hoping to prove that the set of defects less than n had order type ωn, but the best I have so far is that it's at least ωn, and less then ωn+1. Still - well-ordering! And this is basically the LHF[0]! I definitely think we can milk this concept for a bit more.
Maybe we should contact Arias again and tell him we've proved well-ordering? Then look over his paper more carefully and see if we can prove any more of his conjectures. :D (Well, that we should do anyway...)
-Harry
[0]OK, I suppose nobody who wasn't in Tufts House the past few years is going to recognize that acronym[3]. I don't think I've mentioned Nathan's strange acronym-slang anywhere here previously, have I? Well, this one stands for "low-hanging fruit".
[3]Actually, it does show up on acronymfinder.com, so I suppose there are indeed other people out there using them. But I've never seen it elsewhere personally.
Blue Kirby: Someone thought to buy Smash 64 for the Virtual Console for the house's Wii. I think Dan was a bit surprised I was so good at it. :D I realize I'm not by the standards of old Tufts House - I haven't played in quite a while, I keep failing to smash, I never learned to Z-cancel - but I'm certainly good against the people here. Much better than at Brawl, that's for certain. Need to play more, remember more. Took me a bit to remember how to play Falcon.
Obvious-but-funny-anyway-observation: The controls have been modified to match those of Melee. Hence Z-cancelling would now be done with the L button. I don't expect anyone to start referring to it as "L-cancelling", though.
Blue Water Fangs: I was down at GYGO and saw they had the Xbox version of Metal Slug 3 for cheap, so I picked that up. Hooray, Metal Slug 3 with a non-ridiculous number of continues. Heh - this TVTropes page refers to the Xbox version as a "porting disaster" because of this. Bah! If you can't beat a level in five lives, you aren't beating it properly, I say!
Well-ordering: Let's talk about integer complexity. I finally finished classifying n with d(n)≤21d(2), which means I can classify n with D(n)≤1, and... it's terrible. I decided to not even go through and finish it; it may be easy, but it's still not worth it. {n: D(n)=0} has a nice form, so I guess that's worth noting, but {n: D(n)≤1} really doesn't, so... why bother? (OK, I guess I can't say this for *certain* as I didn't finish, but it seems pretty clear.) Well, at least the statement that D(3n)=1 ⇒ D(n)=1 is kind of nice.
But! Stopping work on that means I can actually get back to work on interesting stuff. A few days ago I had the idea to, y'know, actually formalize the notion of certain types of infinite families of integers we'd been using implicitly the whole damn time, and, well it's been very helpful. For instance, we've been able to finally prove that the set of defects is well-ordered! (It has order type ωω.) I was hoping to prove that the set of defects less than n had order type ωn, but the best I have so far is that it's at least ωn, and less then ωn+1. Still - well-ordering! And this is basically the LHF[0]! I definitely think we can milk this concept for a bit more.
Maybe we should contact Arias again and tell him we've proved well-ordering? Then look over his paper more carefully and see if we can prove any more of his conjectures. :D (Well, that we should do anyway...)
-Harry
[0]OK, I suppose nobody who wasn't in Tufts House the past few years is going to recognize that acronym[3]. I don't think I've mentioned Nathan's strange acronym-slang anywhere here previously, have I? Well, this one stands for "low-hanging fruit".
[3]Actually, it does show up on acronymfinder.com, so I suppose there are indeed other people out there using them. But I've never seen it elsewhere personally.
