Notable lists:
The reason why the epsilon delta definition is so venerated is that it fits directly into well known methods of the formalization of mathematics, making the notion completely precise.
Main motivation: Lebesgue integral.
The Bright Side Of Mathematics 2019 playlist: www.youtube.com/watch?v=xZ69KEg7ccU&list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
Approximates an original function by sines. If the function is "well behaved enough", the approximation is to arbitrary precision.
Fourier's original motivation, and a key application, is solving partial differential equations with the Fourier series.
Can only be used to approximate for periodic functions (obviously from its definition!). The Fourier transform however overcomes that restriction:
The Fourier series behaves really nicely in , where it always exists and converges pointwise to the function: Carleson's theorem.
Just by havin the notion of neighbourhood, concepts such as limit and continuity can be defined without the need to specify a precise numerical value to the distance between two points with a metric.
As an example. consider the orthogonal group, which is also naturally a topological space. That group does not usually have a notion of distance defined for it by default. However, we can still talk about certain properties of it, e.g. that the orthogonal group is compact, and that the orthogonal group has two connected components.
Generalize function to allow adding some useful things which people wanted to be classical functions but which are not,
It therefore requires you to redefine and reprove all of calculus.
For this reason, most people are tempted to assume that all the hand wavy intuitive arguments undergrad teachers give are true and just move on with life. And they generally are.
One notable example where distributions pop up are the eigenvectors of the position operator in quantum mechanics, which are given by Dirac delta functions, which is most commonly rigorously defined in terms of distribution.
Distributions are also defined in a way that allows you to do calculus on them. Notably, you can define a derivative, and the derivative of the Heaviside step function is the Dirac delta function.
Key for quantum mechanics, see: mathematical formulation of quantum mechanics, the most important example by far being .
Collections and overviews:
- asciiart.website/index.php?art=people/naked%20ladies "Naked Ladies - Nude Women" category
- if you value medium over content, Ciro found two of the images reproduced in
asciiart.websiteabove also reproduced in the Bitcoin blockchain as described at: ASCII art, that should definitely turn you on, horny nerd
- if you value medium over content, Ciro found two of the images reproduced in
- www.reddit.com/r/ASCII_porn/ on Reddit boring
- www.vice.com/en/article/nepapk/ascii-pr0n-porn-predates-the-internet-but-its-still-everywhere-rule-34 ASCII Porn Predates the Internet But It's Still Everywhere by Vice News (2019)
You just couldn't resist Googling it and clicking this page, could you? You naughty, naughty bearded programmer nerd. Yes, I'm talking to you.
TODO it is quite hard to actually find non-automatically generated ASCII art of people fucking, most of them are just sexy/horny women drawn by bearded nerds, likely and based on sticky physical paper porn magazines from the 80's, good old days.
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Tank Man |
by Ciro Santilli 00 |
2021 CC-BY-SA 4.0 \\ +-|-+
\\/ /|-+o
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/|\\ |/ /oo
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| +-------+oo
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00 | oo oo
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\\/ /|-+o
\\--+ / /o
/|\\ |/ /oo
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| oo+---+ooo
00 | oo oo
\\ +-|-+
\\/ /|-+o
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/|\\ |/ /oo
/ ----- /oo
/ /oo
+-------+oo
oo+---+ooo
oo oo
xx
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/\Code 1. This image depicts the Chinese government fucking 1 million Chinese people in the ass during the Tiananmen Square Protests, which was undoubtedly one of the largest gang bangs of the late 20th century:
The IBM 1401 mainframe runs "Edith" by CuriousMarc
. Source. 1960's punched card ASCII porn. Vintage. EDITH is also mentioned e.g. at: www.threedee.com/jcm/aaa/index.html. No ASCII uploads found however: www.reddit.com/r/programming/comments/a2pser/the_ibm_1401_mainframe_runs_edith/.OMG, Ciro Santilli only learned about this in 2021 after: twitter.com/ryancdotorg/status/1375484757916672000
Pokemon had just launched in Brazil in 1999, 2 years after the Japanese launch: br.historyplay.tv/hoje-na-historia/comeca-exibicao-original-do-anime-pokemon (archive) And Dragon Ball, was first aired in 1989 in Japan! My God, those translations took forever back then!
And everyone was playing Pokemon on their Game Boy Color. Ciro was already cheap however, and didn't buy the console despite wanting it, and just played it through his friends handhelds. But maybe this is a good thing. Playing alone sucks.
Mostly video games of course.
First when he was really young, about 5, Ciro played a lot of NES, but he doesn't remember things from that era very well. Contra, Ninja Turtles, Battle Tanks, Duck Hunt, and some modern "real world jet" top to bottom rail shooter (TODO identify) are definitely some of the games he clearly remembers playing, see also: Figure "Five year old Ciro Santilli playing NES on a joystick". Nintendo hard was truly a thing back then.
As an honorable mention, Ciro remembers his teenage/young adult neighbours in Jundiaí playing some DOS games on their computer, notably there was a 3D racing one. This must have been around 1995/1997, so using some of the very earliest GPUs. Those games felt so incredibly advanced, including the required setup to play them, which required some command-line commands. It felt like some kind of black magic! But Ciro didn't really play them however.
Ciro then skipped the SNES and handhelds, which he played only through friends because he was cheap (but also because Brazil is a poor country remember, and imports are pretty expensive). He clearly remembers playing Super Mario World for the SNES and Pokemon on friends' Gameboys of course.
Ciro then went straight to 5th generation with the Nintendo 64 in 1994 which his parents bought for him during a trip to the United States. Once again, because he was cheap, the only game he bought was Super Mario 64, which likely came with the console? He played that game to death.
Then came Ocarina of Time, which blew everyone's minds, and Ciro would go to Blockbuster to rent it for the weekend, and again play to death with his friends. You had to arrive early at Blockbuster to rent it, otherwise other people would rent all copies!!!
The only time Ciro got robbed as of 2020 was when an older teenager stopped his bicycle in front of Ciro and took his rented Golden Eye 64 copy away from his hand, and run off. Poor drug addict.
Ciro always felt that the PS1 had a much uglier aesthetics than the N64, and didn't like the console. Playing a bit of Final Fantasy VI on his memory did stick deeply to his mind however. Ciro later played all good PS1 RPGs on emulation during University of São Paulo during amazing solitary nights.
And on the PC, Ciro was particularly touched by Age of Empires II and Diablo II.
As a young teenager Ciro would also play Counter-Strike with his friends at LAN houses. Playing that game would make Ciro extremely anxious, his hands got all cold, and it was a lot of fun.
After this Ciro grew up and notice that the only fun game is that of becoming become rich and famous in the real world.
Outside of video games, Ciro got mildly addicted to Magic: The Gathering in his early teens.
There are unlisted articles, also show them or only show them.