All of Joe Zeng's Comments + Replies

I've been looking for something like this for a long time now. I hope Arbital can be the platform that does it well.

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".

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?

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.

Is $N$ itself called $\omega$, 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.

$8$ is not a power of $4$, but ${\log }_{4}8$ is $1.5$. The only thing you prove with $3$ is not a power of $2$ is that $lo{g}_{2}3$ 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 bl... (read more)

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 $N\setminus \{1,2,3,4,5\}$ and the set $5$ both encode the number $1/8$.

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?

Why is it misleading to call injective "one-to-one"?