Math From Scratch 0001: Relations

Bureau 42’s biggest educational project to date begins here. The ultimate goal: teach everything we possibly can in math from the ground up in a sequence of comprehensive lessons, released no more than three weeks apart. This project will likely take years. The first lesson, defining mathematical relations, is available here.

8 replies on “Math From Scratch 0001: Relations”

  1. haupz says:

    Thank you for starting this series. I already liked the quantum physics texts a lot, and am looking forward to reading these.

    I’d like to ask why you chose the hat symbol to represent exclusive disjunction, when it is commonly used to represent conjunction. This might be confusing for readers who have a certain mathematical background. How about using the commonly used “plus in a circle” for exclusive disjunction instead?

    • pythor says:

      I have to agree with haupz. I was taught using that symbol for And, and would be confused by every statement you make using it if it means Exclusive Or. It’s not insurmountable, but it would definitely be annoying.

      Other than that, a good start.

      • I know that the logic symbols have at least three different conventions, depending on whether you are learning them in the context of pure math, philosophy, or computer science. I’ve got three texts on the subject that I used for reference on this one, and went with the conventions that were used by two out of the three. Many of my texts are Dover press due to the great cover prices, but that also means that some of the notations are a bit outdated. Part of the project is to explicitly define every symbol as it’s used, so hopefully there won’t be much confusion. This lesson sets up lesson two, and then will not be explicitly referenced again for at least the rest of the year. (I’m working on lesson 14 now.)

  2. rickyjames says:

    Happy New Year, Blaine and all. As a one-time math nerd and holder of a math degree I have never really used in the real world of industry where I have found myself, I am really looking forward to following this project. Thanks for committing yourself to this project; let the learning begin!

  3. rickyjames says:

    Before we get too far down the rabbit hole, let me mention a very interesting book that I read about five years ago: Where Mathematics Comes From by Lakoff and Nunez. Interesting theory on how the psychology of the human mind is the wellspring of mathematics, not necessarily Incompletely Uncovered Universal Truth. Here’s a wikipedia summary and here’s a pdf of the first four chapters. Something to,er, think about….

  4. TomSwiss says:

    Nice. I do think there’s a typo in the more formal definition of symmetry: should that not read,

    Symmetry: R is symmetric ⇔ ∀a∀b,aRb⇒bRa

    If the characters don’t come thru, that’s

    R is symmetric iff for all a,b aRb implies bRa

    It currently has “and” rather than “implies”.

  5. ashaw says:

    I would like to expose a mistake in your relation definitions.

    The relation ∧ represents logical conjunction otherwise known as the AND relation. For the exclusive or relation you want the ⊻ or ⊕ symbol. see mathworld:

  6. The lesson has now been updated with the standard notations for AND, OR and XOR, and with the typo corrected in the definition of symmetric relations. Thanks all for catching those.

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