Do you think we could have the actual names of the rules as subheadings or as footnotes? Like, at the end of the “Multiplication doesn’t care about the grouping terms” we could write “Mathematicians call this the associative property of multiplication”.
Joe Zeng
Karma: 6
I thought so too when I wrote it up; I put it there as a placeholder for a Wikipedia-style initial definition once we find one that’s more suitable, because I’m having a hard time thinking of one.
I’m meaning to write there, “different authors have wildly different conventions about what constitutes a whole number”. How could that be made clearer?
Made a page of examples here. Tell me what you think.
I’m thinking we should compile a list of sentences or passages that a Math 1 person should be able to read, so people can diagnose for themselves which level of math they’re at rather than relying on purely a sentence to describe them.
I’m thinking we should compile a list of sentences or passages that a Math 2 person should be able to read, so people can diagnose for themselves which level of math they’re at rather than relying on purely a sentence to describe them.
Is itself called , or just the usual ordering of it?
So effectively all order relations are partial order relations?
Hmm… is this a corollary so much as a converse or an addendum? It would be a corollary (by being the contrapositive) if the statement were “Only extraordinary claims require extraordinary evidence”.
I’m thinking the full name of the article should be “Partially ordered set”, with “poset” as an alias and alternate form in the article.
The word “binary predicate” I got from Wikipedia’s article on ordered fields, but it looks like it redirects to “binary relation” anyway, so I’ll change that.
And “comparison operator” is the terminology in computer science (or at least the one commonly used in programming languages); I wasn’t aware that the operator was called an “order” in mathematics in general.
is not a power of , but is . The only thing you prove with is not a power of is that is not an integer.
I think we need a more appropriate definition of Math 0 that doesn’t rely on the negation of some property such as “being actively bad at math”.
It seems like what you really mean by Math 0, outside of that one section of the Bayes’ Rule questionnaire, is “This requisite denotes people who have little to no mathematical skill outside of basic arithmetic and some problem solving,” which is intuitively what makes sense for that level.
I think it’s kind of unnecessary to state that Math 0 people are not averse to numeracy for whatever reason, to specifically block out the people who “hate” math. The Math 0/1/2/3 scale is supposed to be a sliding scale of ability to read mathematical notation and understand some baseline concepts; psychological aversion or active ignorance is another dimension altogether.
For example, somebody might be traumatized by Galois theory due to having an especially hard time learning it in courses, but they’d otherwise be fine learning about anything else. Maybe they were great at math as a kid but then something happened in their adulthood that started making them hate it. In such a case, they’d still be able to understand things, and it’s that exact understanding that traumatizes them. Such a person might even be at a Math 2 level if they hadn’t been traumatized, but this scale places them below Math 0 for an entirely unrelated reason.
It would be a better thing, in my opinion, for us to guide people like these towards resources that can help them get over that aversion, rather than excluding them from Math 0 and telling them to come back when they don’t have that problem anymore.
This definition of the real numbers has a bigger problem with it than just circular logic — it also runs into the 0.9999… = 1 paradox. The sets and the set both encode the number .
Normally the real numbers are defined using either Dedekind cuts or Cauchy sequences of rational numbers. Could we please use one of those definitions instead, as they’re the standard ones used by most mathematicians?
In the body: you as a personal pronoun, y/n?
Why is it misleading to call injective “one-to-one”?
I’ve been looking for something like this for a long time now. I hope Arbital can be the platform that does it well.