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A Ring can be seen as a generalization of a field where:
- multiplication is not necessarily commutative. If this is satisfied, we can call it a commutative ring.
- multiplication may not have inverse elements. If this is satisfied, we can call it a division ring.
The simplest example of a ring which is not a full fledged field and with commutative multiplication are the integers. Notably, no inverses exist except for the identity itself and -1. E.g. the inverse of 2 would be 1/2 which is not in the set. More specifically, the integers are a commutative ring.
The simplest non-commutative, non-division is is the set of all 2x2 matrices of real numbers:Note that is not a ring because you can by addition reach the zero matrix.
- we know that 2x2 matrix multiplication is non-commutative in general
- some 2x2 matrices have a multiplicative inverse, but others don't
As if Greek letters weren't enough, physicists and mathematicians also like to make up tons of symbols, some of which look like the could actually be Greek letters!
Mnemonic: it gives out the amount of fluid that is going in or out of a given volume per unit of time.
Mnemonic: the gradient shows the direction in which the function increases fastest.
Therefore, it has to:
- take a scalar field as input. Otherwise, how do you decide which vector is larger than the other?
- output a vector field that contains the direction in which the scalar increases fastest locally at each point. This has to give out vectors, since we are talking about directions
Can be denoted either by:Our default symbol is going to be:
- the upper case Greek letter delta
- nabla symbol squared
Ciro Santilli thinks that maybe the government does not need to provide those, but it needs to regulate the fuck out of them, notably control over censorship in those platforms: the deplatforming of Donald Trump.
Related:
Things that are not nice such as:
- Taboola, Outbrain, and other chumbox
- BLOBs
- Europe cookie law
- adhesive inside mobile phones and more generally, planned obsolescence
- Jupyter Notebook
- typographical characters that look like ASCII ones, but are not the ASCII ones, e.g. typographical quotes, em-dash. The non-breaking hyphen is not even whitespace, and by def Why not stick to ASCII when ASCII is good enough?
- excessive encapsulation
- replacement of master and slave terminology from technology
- mailing lists. And to add insult to injury, HTML on mailing list messages instead of plaintext.
- blank lines in code added by people trying to increase clarity, especially when there is already indentation for that. Every blank line must be preceded by a line comment explaining what the following block is about, or removed.
- messaging software that force you to have a mobile phone
- advertisements by telephone/SMS
- "state" such as global variables and object members, long live functional programming?
- mosquitoes, the only intrinsically bad thing about tropical countries
- projects with slow compilation times
- Microsoft Windows
- the 2019 Chinese government
- e-learning websites that only allows verified teachers to write content. Cowards who can't handle ranking algorithms.
- domain-specific language
- a build system without an out-of-tree option
- non-linear Git history: stackoverflow.com/questions/20348629/what-are-advantages-of-keeping-linear-history-in-git
- visual programming languages like Scratch. Waste of time. Text programming languages are already equally as visual due to indentation:Just make good serious gamedev libraries and integrated development environments for those real languages instead.
if x == 0: x = 1 - software that prevents you from running as root. Let me fucking shoot myself in the foot if I want to. It is better than having to deal with your hand holding bullshit, which is done in a different way for every project. E.g.: stackoverflow.com/questions/17466017/how-to-solve-you-must-not-be-root-to-run-crosstool-ng-when-using-ct-ng/53099177#53099177
- Medium
- luxury goods
- euphemism
- closed access academic journals are evil
- websites without OAuth
- shower room without a window to the exterior (mould!!!)
- single programs with their interface split across multiple windows, e.g. GIMP, ZynAddSubFX
- graphical user interfaces
- logograms
- infinitesimals. Just use limit instead, please
- country
- knowledge olympiads
- programming languages without a decent dominating package system
- closed source offline software used by millions
- exams
- security through obscurities
- dots in Gmail address
- things in websites that look like links, and behave like links, but don't let you middle click to open them on a separate tab
- K-pop
- numerical computing language
- fiscal paradises
- when the front-end of an website changes an important permanent state, but the URL does not change
- splash screens: you should show boot messages so that people will know what to Google for when things fail. Do you think computer newbies will be afraid and have nightmares?
- milk chocolate: why would you eat that instead of dark chocolate if you are older than 10?
- to talk about something without giving the real name to not scare off the audience
- mathematical symbol that looks like a Greek letter but isn't. Or perhaps mathematical notation in general
- when more than two people gather to play a board game or video game, and two or more people start chatting on and on about random subjects rather than concentrating on the game
- watching television while eating. Same for reading, or doing basically anything else but eat. The only acceptable activity is talking relaxedly, not about work.
- noises coming out of your bicycle. It is so hard to find where they come to fix them!!!
- code drop
- private cars as opposed to public transport. As a cyclist, you can just see the effect that large roads have on nearby areas, it just destroys nature.
- closed standards
- double consonants that make no difference to sound. Dilema? Dilemma? Dillema? Dillemma? Please!
- social media websites that show stuff from people you don't follow when you don't explicitly want that, including things which are not ads, just random suggestions. Twitter starting being like that cirac a 2022. Facebook got worse around that time. It is a constant fight against those stupid websites.
- socks with short legs that don't protect your ankle/lower calf from cold/scratches/dirt, e.g. liner socks
- Presta valves. Why would such a flimsy tech have become so popular compared to the infinitely superior Schrader!
- kimchi
- reverse debugging
- E Ink
- web archiving
- Buildroot
- integrated development environments
- degreaser
- UML: while it might seem like a over-thought thing and likely is, the basic idea that understanding "one to one vs one to many vs many to many" relationships between objects and which object can see which object, is a fantastic approach towards understanding complex object oriented code
- open source software, including open source scientific computing consultancies
- computer
- FOSDEM. Ciro Santilli attended in 2016, and felt extremely good together with all those amazingly smart open source hackers: www.quora.com/What-are-the-best-open-source-conferences/answer/Ciro-Santilli
- Sass
- vimium
- bisection
- vector graphics, notably scalable Vector Graphics
- ASCII art
- OAuth
- command-line interface
- virtualization
- Anusol
- autodidacticism and self-directed learning
- end-to-end encryption
- The Criterion Collection
- version control
- SQLite
- Guerrilla Mail
- POSIX
- static website
- Freeman Dyson
- open access academic publishers
- unconditional basic income
- transhumanism
- 2FA, and notably 2FA apps
- human-readable formats
- wealth tax
- Reproducible builds
- F-Droid
- Can't get you out of my head by Adam Curtis (2021)
- drug liberalization
- Wiki-binge
- molecular Sciences Course of the University of São Paulo
- meal deal
- clade, as opposed to taxonomic ranks
- lingua franca, see also: having more than one natural language is bad for the world
- rsync
- zip hoodies
This section is about functions that operates on arbitrary sets.
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