Sakaé Fuchino @sakaefchn@fedibird.com

#数学 ができない人間が総じて「文系」を自称しているせいで文系の平均レベルが大きく下がっている印象を与える。
君たちは文系ではなく"ただ数学ができない人"です。

The sentence from Borovik's article

«In many countries, politicians, state bureaucrats, theoreticians of mathematics education, and school teachers led by them, made everything possible to turn students into a kind of biorobots trained for passing school exams.»

ought to be discussed and re-discussed by anyone who takes seriously the immense damage inflicted by large publishing companies on mathematical formation.

Several decades after the disaster was started, the results are there, in plain view.

Leibniz based his approach to calculus on infinitesimals - numbers that are bigger than zero but smaller than 1/2, 1/3, 1/4, ... and so on. Many people were uncomfortable with these, so they figured out how to do calculus without infinitesimals. That's how it's usually taught now.

But you can do calculus with infinitesimals in a perfectly rigorous way... and in some ways, it's easier! Here's a free online textbook that teaches calculus this way:

• H. Jerome Keisler, Elementary Calculus, https://people.math.wisc.edu/~hkeisler/calc.html

The picture here is from this book. There's a tiny little infinitesimal number ε, pronounced 'epsilon'. And 1/ε is infinitely big! These aren't 'real numbers' in the usual sense. Sometimes they're called hyperreal numbers:

• Wikipedia, Hyperreal number, https://en.wikipedia.org/wiki/Hyperreal_number

You can calculate the derivative, or rate of change, of a function 𝑓 by doing

(𝑓(𝑥+ε)−𝑓(𝑥))/ε

and then at the end throwing out terms involving ε. For example, suppose

𝑓(𝑥) = 𝑥²

Then to compute its derivative we do

((𝑥+ε)²−𝑥²)/ε

Working this out using algebra, we get

2𝑥+ε

Then, at the end, we throw out the term involving ε and get

2𝑥

This is the rate of change of the function 𝑥².

In 1961 the logician Abraham Robinson showed that hyperreal numbers are just as consistent as ordinary real numbers, and that the two systems are compatible in a certain precise sense. In 1976 Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. And now it's free with a Creative Commons copyright!

『卒業式に自分のルーツがあるブラックヘアーで行くことに、"その時だけブラックヘアーをするのは都合が良い"というコメント』
ってさ

じゃあ卒業式に袴を着る人は年がら年中袴を着てないとだめなのかよ

普段髪をおろしてる人が、卒業式だけ三つ編みにしてたらだめなのかよ

1人の高校生が父親と同じ黒人の伝統的髪形にしたところ、「校則違反」として他の生徒から隔離され、卒業式に出席できず隔離されたニュース。心を痛めたアフリカ系米国人コラムニストの記事から。
『学校の目標は、社会の未来を支える人を育てること。厳格なルールで1人の生徒に『日本は違いを認めない』と態度で示すならば、他の生徒にも『違いは悪いことで、痛みを伴う怖いことだ』と誤ったメッセージを送ることになる。今の時代に求められているのは『違いは自然なことで、変化を避けようとする方が危険だ』と教えることではないか。多様な社会はいつか来るのではなく、既にここにあるのだから』https://mainichi.jp/articles/20230329/k00/00m/040/358000c?utm_source=article&utm_medium=email&utm_campaign=mailhiru&utm_content=20230401

「書店業界は、「文化が失われる」と、自民党の議員連盟に支援を求め、ネット書店の送料無料に対する規制や図書館の新刊本の貸し出しのルール作りなどが検討されている。」

私はわりと本屋で本を買う方だけど、図書館で本を借りる人やネットで本を買う人に嫌がらせをすれば街の書店に客が戻るだろうという発想が気に入らないねえ。

この人らはそのうち古本屋にも嫌がらせを始めるんじゃないか。

やっぱり自民党とつるむとろくでもないことを考えるのだろうか。そういう人らに東西古今の名著を扱ってもらいたくなどないし、そういう人らから本を買うなんて私は願い下げですね。

https://www.asahi.com/articles/ASR3W6309R1KULEI001.html

http://mathcs.albion.edu/scripts/flyer.php?year=2023&month=15&day=23&item=a

I gave a talk today at Albion College on a pigeonhole principle for countable linear orders (the first link should take you to the abstract). The talk was aimed at undergraduates, so I did not get to discuss most of the technicalities. (And there were still a few too many slides.)

Thank you David @drMathArt for the invitation (and dinner). 🙂

The slides can be found at my webpage.

Happy to give additional details if anyone is interested. Rather than publishing them separately, my plan is to include the results in a longer text I am writing.

https://andrescaicedo.wordpress.com/talks/