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by feoren
301 days ago
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> Or you could recognize that "essential" has a meaning in economic/financial terms I do not recognize that. That is the point of my argument. A large portion of economics is rich people trying to justify their own greed as being moral. Classifying goods as "essential" vs. "non-essential" is a way of telling poor people what they're allowed to have, and always has been. A good goes from "non-essential" to "essential" only when rich people are worried they'll get guillotined if the poor don't have access to it. I'm aware that it has a definition in terms of what people are able to stop purchasing when their income goes down, or how consumption relates to income levels in general, but the former is a problematic definition for many reasons, and the latter does not actually coincide particularly well with the categories of goods people list off when they think of "essential goods". Humans in real life just don't respond to changing conditions the same way the little econs in your head do; they way you've decided they "should". Ever heard that humans don't "behave logically"? Yeah, that's economists with overly simplified models being annoyed that (mostly) poor people don't act the way that they've decided poor people should act. See the trend? Ask four economists write out a list of "essential goods" and you'll get five different lists. That is not how definitions work. Ask four mathematicians whether something is a Commutative Ring or not and they'll all agree. That's a definition. "Essential" does not have a definition. Its meaning shifts depending on which group the author of the Wall Street Journal op-ed you're reading wants to villainize this time. |
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Amusingly, there are at least 3 different definitions of commutative ring.
The principal issue is whether it must have a 1 (unity, ie a multiplicative inverse). Wikipedia https://en.wikipedia.org/wiki/Commutative_ring as well as most modern sources insist on this.
Britannica https://www.britannica.com/science/ring-mathematics#ref89421... as well as many older sources (such as Noether's original definition and van der Waerden) do not insist that the ring have a 1. Even first-edition Bourbaki didn't have 1!
Finally, if you do have a 1, then sometimes people include the condition that 0 != 1, ie the trivial/zero ring is deemed not a [commutative] ring. This is somewhat hard to find, but is relatively common among people who specifically define the concept of "ring with identity" (eg Zariski+Samuel). I have also found it unqualified (ie, just in the definition of "commutative ring") in the wild, eg in "Handbook of Mathematical Logic" by Barwise or "The Math You Need" by Mack.
(I agree with people like Conrad and Poonen that rings should have a 1. And I guess that the zero ring is in fact a [commutative] ring.)