Is having a multiplicative inverse an intrinsic property of a number? It seems to be like it’s a property of a number in a context, and second graders are studying the same objects in a different context.

Surely it’s relevant that the 0 point was chosen for sociological reasons that have nothing to do with the data - this is an interval scale, not a ratio scale.

The standard advice about extending to 0 is for ratio scale data (and a justified suspicion that chart makers can’t spot the difference).

The five year old should be asleep, but has figured out that I’ll break the no conversations after bedtime rule if they misuse material implication.

The power of material implication is in convincing the four year old that since annis hags aren’t real, that means if they meet an annis hag then they’ll be able to do real magic to escape it.

I seem to recall something about a freeze except for critical positions, and hearing about how departments were going without administrative support because they weren't allowed to replace retiring staff.

To be fair, our HR platform was already plenty shitty before it got LLM-ified.

Oh, that indeed looks like it works.

It's not obvious to me that there's an immediate answer from the syntactic form of the statement. I *suspect* the answer is no, because the values of the unique solution are close enough to definable using an integral which can be expressed in a first-order way, but it requires at least some work.

This is going to depend a bit on what you mean. For *any* theorem about the reals, sufficiently robust non-standard extensions will satisfy the analogous theorem (in this case, every *internal* f with suitable other properties gives an ODE with a unique *internal* solution).

Definitely.

But the g you’ve defined isn’t *f, so there’s no reason to think the derivative it gives you is the derivative of f.

*f isn’t uniquely determined, but it is pretty constrained. In particular, being differentiable is basically equivalent to saying that the derivative is determined.

There’s not a unique way to extend to *R. (Indeed, the statement doesn’t really make sense, because *R doesn’t describe a unique object.)

But you don’t need that, because the facts you care about *are* determined. (Ultraproducts don’t change this, because they’re also not unique.)

It’s not a restriction at all, because you can always expand your language to include whatever function you want. All of calculus survives.

A colleague discussed his notes from a meeting about a new policy with me; next to the words "hopes and fears" on the handout was a little note of what had been said at the meeting - "blow it all up".

He clarified that this was a hope.

I’m reasonably sure a lot of students were using it during our last day of class no stakes final exam review game last semester.

Is was told they named it Workday because that’s how long it takes to do anything in it.

Also lots of random interruptions to monologue about their character's backstory.

The four year old persuaded me to run a D&D module for them as a 'choose your own adventure' type game.

They proceeded to ignore every plot hook but found a random NPC and decided they were best friends now. Clearly a natural gamer.

You can sort of see how he might have mangled the studies that are out there into this - Pew says the median number of close friends is between 3 and 4 (www.google.com/url?sa=t&sou...) though other studies (journals.plos.org/plosone/arti...) report higher numbers.

As someone who’s definitely used that example, I’m curious why. (Especially why one would prefer forcing CH when that’s not needed to establish the consistency of CH, and historically not how it was first established.)

It’s only on the faculty listserv if it’s actually on the listserv. This is just sparkling reply all rants.

There are lots of models of V=L; CH is true in all of them. If you’re sitting in some fixed universe of ZFC, there’s a single L which is the unique constructible inner model of this model. But there are other models of ZFC, and they have their own versions of L. (All satisfying CH.)

I think the uniqueness you’re thinking of says that *given a particular model V of ZFC* there’s a unique inner model of V=L. But there are many different models of ZFC which give rise to different versions of L.

It definitely doesn’t have only one model. For instance, it has nonstandard models which contain ill-founded sets (which the model doesn’t know are ill-founded); in some cases, those ill-founded sets appear in the model to be nonstandard proofs of the sentence you asked about.

Relatedly, being in the model L isn’t really significant here; arithmetic facts like probability are absolute between inner models - whatever your model of V, the corresponding of model of L will agree about which things are provable.

True, because it’s indeed not provably. (And, relatedly, not provably so from ZFC+V=L.)

Canvas has a systematic hostility to labeling things accurately that seems too consistent to be an accident.

There’s a specific sense of dread that comes with picking your child up from preschool and seeing that a third of the class didn’t show up today.

I’ve been using Mileti’s new-ish book, which I think is pitched similarly to Mileti, but isn’t quite as concise, and has a bit more optional material on more advanced topics.

Math papers vary between these two conventions, and the economics one seems much better to me: when you encounter a technical term somewhere in the middle of the paper, you know where to flip to, instead of having to search for the first use. (Who reads papers in linear order anyway?)