Municipal steam networks are still operating today.

For new infrastructure, Electricity is just so good-enough, that it is hard to justify building out partial alternatives like steam pipes. But where we already have them, they are still useful.

Where in those axioms does it say that ↑ = 0∗ = 0 {0 0 } is not a number? No where, that’s where!

The actual reason that ↑ is simply that it is too ill behaved. The stuff I thought were the “numbers” of combinatorical game are actually just called Conway games. Conway numbers are defined very almost identically to Conway games, but with an added constraint that makes them a much better behaved subset of Conway games.

I suppose you could call this an axiom of combinatorical game theory; but at that point you are essentially just calling every definition an axiom.

<s> Getting back to my original point; this distinction just goes to show how small minded mathematicians are! Under Conway’s supposed “reasonable” definition of a number, nimbers are merely games, not proper numbers. However, the nimbers are a perfectly good infinite field of characteristic 2. You can’t seriously expect me to believe that those are not numbers! </s>

I was going to make a comment about surreal numbers not being numbers. But I did a bit of fact checking and it looks like all of the values I was objecting to are not considered surreal numbers, but rather pseudo numbers.

I find this outrageous. Why can’t ↑ be a number? What even is a number that would exclude it and leave in all of your so-called numbers?

I’m going to take this as an opportunity to point out that bees are a type of fish in California.

You get this property in algrabraic structures called “wheels”. The simplest to understand wheel is probably the wheel of fractions, which is a slightly different way of defining fractions that allows division by 0.

The effect of this is to create 2 additional numbers: ∞ = z/0 for z != 0, ⊥, and ⊥ = 0/0.

Just add infinity gives you the real projective line (or Riemen Sphere if you are working with comples numbers). In this structure, 0 * ∞ is undefined, so is not quite what you want

⊥ (bottom) in a wheel can be thought as filling in for all remaining undefined results. In particular, any operation involving ⊥ results in ⊥. This includes the identity: 0 * ⊥ = ⊥.

As far as useful applications go, there are not many. The only time I’ve ever seen wheels come up when getting my math degree was just a mistake in defining fractions.

In computer science however, you do see something along these lines. The most common example is floating point numbers. These numbers often include ∞, -∞ and NaN, where NaN is essentially just ⊥. In particular, 0 * NaN = NaN, also 0 * ∞ = ⊥. The main benefit here is that arithmetic operations are always defined.

I’ve also seen an arbitrary precision fraction library that actually implemented something similar to the wheel of fractions described above (albeit with a distinction between positive and negative infinity). This would also give you 0 * ∞ = ⊥ and 0 * ⊥ = ⊥. Again, by adding ⊥ as a proper value, you could simplify the handling of some computations that might fail.

It’s common enough that my State’s toll provider has had a banner on their front page about it for months https://www.driveezmd.com/

If you want to file a complaint, the Internet crime control center is asking for information on these scams specifically https://www.ic3.gov/PSA/2024/PSA240412

Don’t, Jadzia clearly appreciated it.

Trill’s relationships to their past hosts is complicated and never fully explored, but it is clearly established that the distance they create between their current host’s life and that of their past host is something that is enforced apon them by broader trill society.

Both Kurzon and Jadzia were, at least at times, clearly unhappy at the extent to which they had to distance themselves from their past life.

https://youtu.be/Qu-bP5367Yo?si=YNBFC_IUo7o7FpCd

The thing is, Trill are not trans. Dax didn’t go from being a man to a woman. Kurzon was always a man and Jadzia was always a women. And DS9 actually took this concept seriously on its own terms.

The BBC also doesn’t call them terrorists:

https://www.bbc.com/news/world-middle-east-67083432

“The United States is not in the business of interfering in other people’s affairs”

“Since when Sir?”