| Lemma 2: ("Real Induction") Let A be a subset of real numbers. | |
| If | |
| (0) α ∈ A | |
| (1) ∀x ∈ A. ∃y. [x,y) ⊆ A | |
| (2) ∀xy. [x, y) ⊆ A ⇒ y ∈ A | |
| then [α,∞) ⊆ A. | |
| Proof: | |
| Suppose towards a contradiction that [α,∞) ∖ A is nonempty. Set β = inf ([α,∞) ∖ A). | |
| (1) means we can't have β ∈ A, because it would collide with the infimum. |
| /*** | |
| * A little bit of research into what would be needed for a "direct manipulation" toy in emacs. | |
| * - NodeJS allows replacing `Error.prepareStackStrace` with a custom handler that can obtain | |
| * first-class stack trace data. | |
| * - An arbitrary function call (see below, `knob(1429)` for example) can obtain a stack | |
| * trace and inspect it to find out where in the file the actual call to knob(1429) took place. | |
| * - Since we're in typescript, we can also find the sourcemap and use it to map this into | |
| * a location into the original `.ts` file. | |
| * - We can shell out to emacsclient to evaluate arbitrary elisp | |
| * - It can in turn go to the appropriate place in the active buffer viewing the `.ts` file, |
| // g++ -I/usr/local/include/SDL2 -I/usr/include/GL b.cc -lSDL2 -lGL -lGLU -o b | |
| #include <SDL2/SDL.h> | |
| #include <SDL2/SDL_opengl.h> | |
| #include <gl.h> | |
| static SDL_Window *window; | |
| static SDL_Renderer *renderer; | |
| #define width 640 |
| const W = 52; | |
| const H = 30; | |
| const MAX_ITER = 1000; | |
| function iters(cr, ci) { | |
| let zi = 0; | |
| let zr = 0; | |
| for (let i = 0; i < MAX_ITER; i++) { | |
| [zr, zi] = [zr * zr - zi * zi + cr, 2 * zr * zi + ci]; | |
| if (zr * zr + zi * zi > 16.0) return i; |
| 5403 Friendship Avenue. | |
| Henry Wright Fisher loĝis ĉi tie en 1912. | |
| Sr. Fisher naskiĝis en Youghal, Ireland, Januaro 31, 1861, la filo de | |
| Abram kaj Sara (Wright) Fisher. Li alvenis al Usono je 1874, kaj post | |
| dekkvar jaroj, ricevis diplomon pri mekanika inĝenierarto de la | |
| universitato Cornell. Post diplomiĝo, li ligiĝis kun la entrepreno | |
| Bergman & Co. kaj la C. & C. Motor Company, kaj poste eniris la | |
| servicon de Standard Underground Cable Company, fariĝinte ĝia |
| # # I ran the following perl script on the file | |
| # # https://www.unicode.org/Public/UCD/latest/ucd/UnicodeData.txt: | |
| # | |
| # #!/usr/bin/perl | |
| # | |
| # use charnames(); | |
| # use utf8; | |
| # use open qw( :std :encoding(UTF-8) ); | |
| # use File::Basename; | |
| # |
| import { Point, rot90, rotate, vdiv, vdot, vplus, vscale } from './point'; | |
| const NARROW_COLOR = '#ffffff'; | |
| const WIDE_COLOR = '#7777ff'; | |
| const BG_COLOR = WIDE_COLOR; // '#dff'; | |
| const LINE_WIDTH = 0.25; | |
| const width = 1024; | |
| const height = 768; | |
| const OFF_MIN = -9; |
| # GIMP 'Curves' settings | |
| (time 0) | |
| (linear no) | |
| (channel value) | |
| (curve | |
| (curve-type smooth) | |
| (n-points 17) | |
| (points 34 0.000000 0.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 1.000000 1.000000) | |
| (n-samples 256) |
| function prodf(xs, ys, f) { | |
| const rv = []; | |
| for (let i = 0; i < xs.length; i++) { | |
| for (let j = 0; j < ys.length; j++) { | |
| rv.push(f(xs[i], ys[j])); | |
| } | |
| } | |
| return rv; | |
| } |
Welcome to imaginary book club! I hope everyone finished the reading this week. No? Fine, we'll just wing it. At least there's snacks.
There is a deck of cards. Each has a question on it. Play starts with a random player and proceeds in a circle, with each player drawing a card and answering the question. The first two are always:
