# What is the point of teaching kids set theory? **URL:** \ **Category:** Factual Questions\ **Created:** [October 18, 2019, 2:03pm UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955 "2019-10-18T14:03:25Z")\ **Posts on this page:** 11\ **Page:** 5
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [October 29, 2019, 4:18pm UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/81 "2019-10-29T16:18:34Z")
> [@Spectre\_of\_Pithecanthropus](#): > > ETA: We also had expanded notation, e.g. 5824=5_1000×8_100+2_10+4_1. > > However neither in grade school arithmetic nor in high school algebra was the obvious connection made with single variable polynomials in algebra. At both times, math seemed to me like a random bag of tricks that I was meant to use without being told why they worked. For instance, I was taught that of the digits of a number in base 10 add up to a multiple of 9, then the entire number is also divisible by 9. But I’m pretty sure I was never taught _why_ that works. Had I had any explanations of math beyond basic arithmetic I might have learned something about it. But I forgot that bag of tricks soon after learning them because they had no application I could imagine at the time. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [October 29, 2019, 4:39pm UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/82 "2019-10-29T16:39:43Z")
> [@TriPolar](#): > > Had I had any explanations of math beyond basic arithmetic I might have learned something about it. But I forgot that bag of tricks soon after learning them because they had no application I could imagine at the time. Am I the only one that still occasionally(\*) “casts out nines” to check the results of a column addition or long multiplication? (\* - Well, I used to do this routinely. But I’m not sure I’ve done it in the last decade or two unless it was to teach the trick to my kids.) ETA: Yes! I’ve done it to check Yahtzee score totals! ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [October 29, 2019, 4:46pm UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/83 "2019-10-29T16:46:07Z")
Given the number of people I see who fail to understand major, important issues, or who struggle with reading comprehension, because they cannot get really fundamental set theory, I’d say the schools aren’t teaching enough of it. Math isn’t just math. Math serves as practice for the mind to understand logic. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [October 29, 2019, 5:42pm UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/84 "2019-10-29T17:42:26Z")
> [@septimus](#): > > Am I the only one that still occasionally(\*) “casts out nines” to check the results of a column addition or long multiplication? When I was a kid, they never taught us about this in school. I ran across the technique in a math book I checked out from the library (yes, I was that kind of kid) and thought, “Wow, that’s cool! And useful! How come they didn’t teach us this?” ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [October 29, 2019, 6:03pm UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/85 "2019-10-29T18:03:27Z")
> [@Thudlow\_Boink](#): > > When I was a kid, they never taught us about this in school. I ran across the technique in a math book I checked out from the library (yes, I was that kind of kid) and thought, “Wow, that’s cool! And useful! How come they didn’t teach us this?” I’m looking at it now, and I am really glad we didn’t learn this; it’s as complicated a process as doing the problem in the first place, and would add a new way to make an error. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [October 30, 2019, 2:22am UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/86 "2019-10-30T02:22:10Z")
> [@RickJay](#): > > Math isn’t just math. Math serves as practice for the mind to understand logic. A lot of logic _is_ mathematical. They even call it “mathematical logic” (a term which can include set theory). But I do not see how one can make it through elementary school without even a superficial introduction to arguments in logical form, even for something like simple Euclidean geometry or writing certain types of essays. It is also a core liberal art, to the extent that influences primary and secondary curricula. ---
**Author:** ![glowacks](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/glowacks/32/5548_2.png) [@glowacks](https://boards.straightdope.com/u/glowacks)\ **Post date:** [November 2, 2019, 4:59am UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/88 "2019-11-02T04:59:52Z")
> [@RickJay](#): > > I’m looking at it now, and I am really glad we didn’t learn this; it’s as complicated a process as doing the problem in the first place, and would add a new way to make an error. Often the best way to check whether you got the right answer is to do it in two different ways. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [November 2, 2019, 5:53am UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/89 "2019-11-02T05:53:52Z")
> [@RickJay](#): > > I’m looking at it now, and I am really glad we didn’t learn this; it’s as complicated a process as doing the problem in the first place, and would add a new way to make an error. I don’t know where you looked at “casting out nines,” but it’s not complicated, and catches errors with very high probability. One might need to practice with it a bit before drawing conclusions. For example, let’s suppose I wonder how many centimeters there are in the circumference of a circle with one-inch diameter. It might be easier to work this by hand instead of looking for a calculator. 3.14159265 × 2.54000000 = 7.979645331 Whoa! That involved so much work that an error might have crept in! Let’s cast out nines: [del][COLOR=“Red”]3.141[/del][/COLOR]5[del][COLOR=“red”]9[/del][/COLOR]265 × 2.[del][COLOR=“red”]54[/del][/COLOR] = 7.[del][COLOR=“red”]9[/del][/COLOR]7[del][COLOR=“red”]9[/del][/COLOR]6[del][COLOR=“red”]45[/del][/COLOR]331 No arithmetic. Just wherever you see a ‘9’ (or a ‘45’ or ‘18’ etc.) you cross it out. (In practice there are even easier ways to cast out nines.) Let’s rewrite the work with the crossed out numbers not shown: 5 2 65 × 2 = 7 7 6 33 1 Now continue the process. While looking for nines on the left you notice the whole group of digits sums to 18. 1+8 … a multiple of nine; cast out the whole thing. Similarly the right side group sums to 27; 2+7 is another multiple of nine. We’re left with 0 × 2 = 0 Yep, the arithmetic checks. Checking it was _much_ easier than the original 3.14159265 × 2.54000000 = 7.979645331. ---
**Author:** ![Crossbreed](https://avatars.discourse-cdn.com/v4/letter/c/a4c791/32.png) [@Crossbreed](https://boards.straightdope.com/u/Crossbreed)\ **Post date:** [November 2, 2019, 9:26am UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/90 "2019-11-02T09:26:18Z")
That is because For y = the sum of the digits in x, y mod 9 = x mod 9 That trait seems to hold true for _every_ integer base (b). y mod (b-1) = x mod (b-1) ---
**Author:** ![Melbourne](https://avatars.discourse-cdn.com/v4/letter/m/b5e925/32.png) [@Melbourne](https://boards.straightdope.com/u/Melbourne)\ **Post date:** [November 7, 2019, 6:06am UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/91 "2019-11-07T06:06:27Z")
> [@BigT](#): > > Melbourne, simply Googling “exterior angles” will tell you that you are wrong about what that term means. Google itself says “the angle between a side of a rectilinear figure and an adjacent side extended outward.” Wikipedia has an article showing the concept. Multiple math articles are shown where they discuss it. All agree with this definition. > > The fact that the exterior angles add up to 360 on any convex polygon is something that is part of the basic geometry curriculum. The fact that you get a different answer shows that you are not using the correct definition. > > The internal and external angles add up to 180 degrees. That is how the terms are defined. You appear to be mixing up that, for instance, a 90 degree angle is also a -270 degree angle. You use the negative sign when going backwards. I have no Greek at all, which is perhaps why the Euclid I saw did not use negative numbers. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 7, 2019, 1:40pm UTC](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955/92 "2019-11-07T13:40:56Z")
Knowing Greek wouldn’t help. The oldest surviving copies we have of _The Elements_ are in Arabic. Of course, the language isn’t the important part, anyway. [Previous page](https://boards.straightdope.com/t/what-is-the-point-of-teaching-kids-set-theory/841955.md?page=4)