Ancestors

Written by lcamtuf :verified: :verified: :verified: on 2024-09-03 at 04:29

Ah yes, I remember buying that textbook

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Written by Jeffrey Goldberg on 2024-09-03 at 04:42

@lcamtuf, Chapter 1 defines numbers, some common mathematical notation, and a few other things that give you hope that you can read this book.

You might get through Chapter two.

By Chapter 3, you,put it on the shelve with all your other Springer textbooks.

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Written by jonathankoren™ on 2024-09-03 at 05:42

@jpgoldberg @lcamtuf Springer books are like the math entries on Wikipedia. They’re both places where people are in a competition to make themselves as baroque and not just esoteric, but practically occult as possible.

Now excuse me, I have to finish replacing the word “one”with“unity”

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Toot

Written by John Carlos Baez on 2024-09-07 at 21:40

@jonathankoren - they're actually not trying to be baroque, they are just mathematicians talking the only way they know how. I know: I'm a mathematician, and I find these entries generally quite clear. The problem is, it's hard to get mathematicians to write in ways that nonmathematicians can understand. At least the first paragraph should be aimed at everyone.

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Descendants

Written by jonathankoren™ on 2024-09-07 at 22:41

@johncarlosbaez

• Stares in “sums to unity”*

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Written by John Carlos Baez on 2024-09-07 at 23:57

@jonathankoren - sums to unity, adds to one - same thing to us weirdos. Feel free to change it to "sums to one"!

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Written by Mark Dominus on 2024-09-08 at 16:02

@johncarlosbaez @jonathankoren I thought the reason for that was that "sums to one" invites the question "sums to one what?"

In some contexts it could be really misleading. "a series of dyadic fractions that sums to one" could mean "a series of dyadic fractions that sums to unity" or "a series of dyadic fractions that sums to a dyadic fraction".

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Written by John Carlos Baez on 2024-09-08 at 16:28

@mjd @jonathankoren - okay, that's a decent reason for using "sums to unity". I would never dream of interpreting "sums to one" to mean "sums to one of those things I was just talking about", and anyone using it to mean that is really asking for trouble. But I agree that it's good to completely eliminate ambiguity when writing math.

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Written by Mark Dominus on 2024-09-08 at 17:13

@johncarlosbaez @jonathankoren I think it dates from a time when grammatical patterns were different: sentences were longer and distant anaphoras were more common. Also a time when the unambiguous "sums to 1" would have looked more uncouth.

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Written by Jeffrey Goldberg on 2024-11-10 at 18:18

@mjd @johncarlosbaez @jonathankoren

I thought that this goes back to (at least) the Pythagoreans. For them unity was not a number. And it’s only since Frege’s definition of the integers that one is clearly a number.

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Written by Mark Dominus on 2024-11-10 at 18:24

@jpgoldberg @johncarlosbaez @jonathankoren The Treviso Arithmetic of 1478 says explicitly that 1 is not a number.

But I find your suggestion of Frege hard to understand. Are you reallly saying that Gauss wouldn't certainly have considered 1 a number? Cauchy? Legendre?

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Written by Jeffrey Goldberg on 2024-11-11 at 01:03

@mjd @johncarlosbaez @jonathankoren

I never meant to say that Gauss et al wouldn’t consider 1 a number. I wasn’t trying to suggest that Frege is responsible for 1 being considered a number, but I do see how that could follow from what I wrote.

I am ignorant of when 1 became fully accepted as a number, and so I shouldn’t have written something that carries the implicature that it is “only since Frege.”

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Written by Chris Fox on 2025-01-18 at 16:51

@mjd @johncarlosbaez @jonathankoren One thinks it is because 'one' refers to oneself.

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Written by Benjamin Geer on 2024-10-01 at 11:35

@johncarlosbaez @jonathankoren Donald Knuth’s Concrete Mathematics makes me think that maybe computer scientists are generally better at writing maths textbooks than mathematicians are.

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Written by John Carlos Baez on 2024-10-01 at 16:41

@benjamingeer @jonathankoren - "Generally", eh? Do you have more than one example?

It's a great book, but Knuth happens to be a great writer, writing about one of the things he knows best. Also, "concrete" mathematics is a lot easier to explain to people who already know calculus than anything like abstract algebra, topology, real analysis, and so on - the main topics in upper-level undergraduate math courses.

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Written by Benjamin Geer on 2024-10-01 at 18:15

@johncarlosbaez @jonathankoren I’m definitely overgeneralising from a sample size of 1 😄

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