set symbolism suppression

eliminating the middle, man (06/07)
was my third post (in vlorbik
on math ed
, as this site
was first known [to 01/10.
next was MathEdZineBlog, to 01/13;
then a grader’s notes]). my fourth post
was {X : X is full of baloney} (06/07).

these were published as a two-parter
with the (dull, dull) title textbooks
and notations
. the badness of
standard-text “set builder” notation
(the topic of the latter) had, for
quite a while, been a burning issue
for me; my then-recent discovery of the
attack on the “sign of intersection”
(the topic of the former) nudged me
into finally ranting that rant online.

so there’s some evidence that at least part
of why i *began* mathblogging when i did
was the need to announce that i’d been
newly horrified by new depths achieved
by the enemies of clarity in the long-
-established Notation Wars.

much more recently, i was horrified
anew: in the sloppily-ranted (and,
again, boringly-titled) midterm report
of 11/12, i announced my discovery
that The Enemy had come for the set-inclusion
symbol in my favorite intro-to-*real*-math
course (“linear algebra”).

the rest of the notations file is mostly
more about notations themselves than
Notation Wars. i haven’t been very good
about tagging my posts.

along the way, there was capital script-D of f,
(01/09) pointing out (among other things)
that remedial-algebra courses
daring even to *mention* “domains”
and “ranges” really (reallyreally)
ought to also introduce *symbols*
for these objects. (*easily written*
symbols, of course.)

somewhere i may even already have indicated
one high-hope-against-all-lack-of-hope: early
(and correct, and consistent) use of (the standard)
f: D \rightarrow C
notation (for a function f with domain
D and co-domain C). as scary as that
might be. (once the actual students
actually see how useful “careful use
of code” actually *is*, they’ll grab
it when they need it… more and more.
this is part of what’s called “getting
good”.)

anyhow, i guess i’m just circling wagons
right in here. there’s some sign-of-equality
stuff by me in the blog next door, for instance.
and i’m feeling a need to have the evidence
(that Textbook Set Theory, long dying of
a usually-fatal illness, has been mortally
wounded in the bargain and is sinking fast)
much better organized (and, just maybe,
somewhat more level-headedly presented).

but not right away, not now.

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  1. somebody else

    https://vlorbik.wordpress.com/2010/01/13/partial-contents-version-ii/
    covers vlorbik on math ed
    from “first post” (06/07/07)
    to “i quit” (02/24/09).
    [~49 titles linked (chrono order)]

    (& mathy open a vein selecta
    from “open letter at random” (08/09/09)
    to “now here’s something…” (11/23/10):
    rambles and zines and sets and finite
    geometries and…
    [~23 titles linked; chrono])

    http://vmescratch.wordpress.com/2009/11/23/97/
    148: pre-calculus
    (VME had lots about work with certain 148’ers;
    i wrapped up the quarter here after quitting VME)
    from “as i was saying” (02/06/09)…
    through much ado about log & exp…
    and a bunch of links… etcetera..
    to “last post” (03/17/09)
    [~19 TLC]

    https://vlorbik.wordpress.com/2010/12/01/community-college-calculus/
    [~16 TLC]

    http://vlorblog.wordpress.com/2010/01/02/posted-in-09/
    there’s considerable overlapping at first
    with other blogs; from august to december
    it’s all open a vein (“vlorblog”
    in the URL… currently dead letters).
    [~39 TLC]

    http://vlorblog.wordpress.com/2010/11/28/posted-in-2010-early-edit/
    open a vein was winding down
    by about may; the archives will reveal more.
    [~23 TLC]

    http://vlorblog.wordpress.com/2012/08/29/posted-in-2011-2012/
    january of ’11 through june ’12;
    the slow death of OAV.
    [12 TLC]

    still left to do:

    *index owen’s cooking show (12/12–02/13)
    (the best current draft is
    the daadd file
    [domestic arts in the age of digital distribution]).

    *jam everything together in one big
    no-need for meta-index-at-all post

    *seek (and work to create) some easily-
    -followed threads through a few of the
    big topics.

  2. Owen Thomas8:02 PM

    +Andrew Dunnells the standard treatment in the pros is called ZF … zermello-frankel at an approximation but i’m lazy to look it up. the “peano postulates” for the Natural Numbers are more or less replaced on this treatment with the “ordinals” 0 := {}, 1 := {0}, 2={0,1}, and so on… with each ordinal defined (speaking somewhat loosely) as the set-of-ordinals-less-than-itself.
    the “smallest” infinite cardinal on this model is then {0, 1, 2, 3, …}.
    i pause to remark that, being expanded, one has (useless for larger examples; i suppose writing out “3” on this model is a good exercise) code like { {}, { {} }, { {}, {{}} }, …}: “it’s set-theory all the way down”, one might say. thus far the concepts of “ordinal” and “cardinal” coincide. with a little slight-of-hand the same trick… define objects by collecting together all the “lesser” objects… works for “bigger” infinite sets (like the continuum… or P(N) [the power set of the naturals]). i’d better quit and take a breath here.
    Show less

    Owen Thomas8:07 PM

    1
    Edit

    the “cardinality of the continuum”… c as often as not… is the same as that of the irrationals. “cantor’s continuum problem” was to decide whether there are infinite cardinalities between Card(N) (“aleph-null” in the lit) and c. it turns out this is “undecidable” (in the sense that one may “construct models” of set theory either way; it depends what axiom system we use, in other words). fascinating stuff, in my opinion.




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