*"Next time you're considering [offing yourself](suicide.md), go for it."* --genuine reaction of normal people in Xonotic to drummyfish advocating people should love each other
*"Next time you're considering [offing yourself](suicide.md), go for it."* --genuine reaction of normal people in [Xonotic](xonotic.md) to drummyfish advocating people should love each other
{ My email is currently: drummyfish AT disroot DOT org. ~drummyfish }
Drummyfish (also known as *tastyfish*, *drummy*, *drumy*, *smellyfish* and *i forcefeed my diarrhea to capitalism*) is a [programmer](programming.md), [anarchopacifist](anpac.md) and proponent of [free software/culture](free_software.md), who started [this wiki](lrs_wiki.md) and invented the kind of software it focuses on: [less retarded software](lrs.md) (LRS). Besides others he has written [Anarch](anarch.md), [small3dlib](small3dlib.md), [raycastlib](raycastlib.md), [smallchesslib](smallchesslib.md), [tinyphysicsengine](tinyphysicsengine.md), [SAF](saf.md) and [comun](comun.md). He has also been creating free culture art and otherwise contributing to free projects such as [OpenMW](openm.md); he's been contributing with [public domain](pd.md) art of all kind (2D, 3D, music, ...) and writings to [Wikipedia](wikipedia.md) (no longer cause ban), [Wikimedia Commons](wm_commons.md) (also banned now), [opengameart](oga.md), [libregamewiki](lgw.md), freesound and others. Drummyfish is insane/neuroretarded, suffering from anxiety/[depression](depression.md)/etcetc. (diagnosed [avoidant personality disorder](avpd.md)) and has more than once been called a [schizo](schizo.md), though psychiatrists didn't officially diagnose him with schizophrenia (yet). He sometimes [self harms](self_harm.md), both physically and socially. Due to spreading uncensored truth, helping and loving others and revealing corruption he is banned and censored on many places on the Internet, including [Wikipedia](wikipedia.md), Wikimedia Commons, [4chan](4chan.md), [GitLab](gitlab.md), many [subreddits](reddit.md), some [Xonotic](xonotic.md) and [Openarena](openarena.md) servers etc. He also has no [real life](irl.md) and is pretty retarded when it comes to leading projects or otherwise dealing with people or practical life. Drummyfish's political compass is off the charts, he once tried to take the political compass test, the computer got confused and exploded. He is also a [wizard](wizard.md).
Drummyfish (also known as *tastyfish*, *drummy*, *drumy*, *smellyfish* and *i forcefeed my diarrhea to capitalism*) is a [programmer](programming.md), [anarchopacifist](anpac.md), wannabe [generalist](generalism.md) and proponent of [free software/culture](free_software.md), who started [this wiki](lrs_wiki.md) and invented the kind of software it focuses on: [less retarded software](lrs.md) (LRS). Besides others he has written [Anarch](anarch.md), [small3dlib](small3dlib.md), [raycastlib](raycastlib.md), [smallchesslib](smallchesslib.md), [tinyphysicsengine](tinyphysicsengine.md), [SAF](saf.md) and [comun](comun.md). He has also been creating [free culture](free_culture.md)[art](art.md) and otherwise contributing to free projects such as [OpenMW](openm.md); he's been contributing with [public domain](pd.md) art of all kind (2D, 3D, music, ...) and writings to [Wikipedia](wikipedia.md) (no longer cause ban), [Wikimedia Commons](wm_commons.md) (also banned now), [opengameart](oga.md), [libregamewiki](lgw.md), freesound and others. Drummyfish is insane/neuroretarded, suffering from anxiety/[depression](depression.md)/etcetc. (diagnosed [avoidant personality disorder](avpd.md)) and has more than once been called a [schizo](schizo.md), though psychiatrists didn't officially diagnose him with schizophrenia (yet). He sometimes [self harms](self_harm.md), both physically and socially. Due to spreading uncensored truth, helping and loving others and revealing corruption he is banned and censored on many places on the Internet, including [Wikipedia](wikipedia.md), Wikimedia Commons, [4chan](4chan.md), [GitLab](gitlab.md), many [subreddits](reddit.md), some [Xonotic](xonotic.md) and [Openarena](openarena.md) servers etc. He also has no [real life](irl.md) and is pretty retarded when it comes to leading projects or otherwise dealing with people or practical life. Drummyfish's political compass is off the charts, he once tried to take the political compass test, the computer got confused and exploded. He is also a [wizard](wizard.md).
**Drummyfish is the most physically disgusting bastard on [Earth](earth.md)**, no [woman](woman.md) ever loved him, he is so ugly people get suicidal thoughts from seeing any part of him.
@ -90,7 +90,7 @@ At the beginning of 1991 [Tim Berners-Lee](berners_lee.md) created the **[World
Shortly after the **[Soviet Union](ussr.md) dissolved** and on 25 August 1991 **[Linus Torvalds](linus_torvalds.md) announced [Linux](linux.md)**, his project for a completely [free as in freedom](free_software.md) Unix-like [operating system](os.md) kernel. Linux would become part of [GNU](gnu.md) and later one of the biggest and most successful software projects in history. It would end up powering Internet servers and supercomputers as well as desktop computers of a great number of users. Linux proved that free software works and surpasses proprietary systems.
After this very recent history follows, it's hard to judge which recent events will be of historical significance much later. 1990s have seen a huge growth of computer power, video [games](game.md) such as [Doom](doom.md) led to development of [GPU](gpu.md)s and high quality computer graphics along with a wide adoption of computers by common people, which in turn helped the further growth of Internet. In around mid 90s the [web](www.md) overtook [gopher](gopher.md) in popularity and started to become the forefront of the Internet. Late 90s saw the rise of the ["open source" movement](open_source.md) ([OSI](osi.md) was established in 1998). Year 2000 was infamously preceded by the [Y2K](y2k.md) hysteria, the [fear](fear_culture.md) of technological [collapse](collapse.md) that was to be caused by computers flipping from year 99 to 00 -- this of course didn't happen. Shortly after 2000 [Lawrence Lessig](lessig.md) founded [Creative Commons](creative_commons.md), an organization that came hand in hand with the [free culture](free_culture.md) movement inspired by the [free software movement](free_software.md). At this point over 50% of US households had a computer. From 2005 we've seen a boom of [social networks](social_net.md) like [Facebook](facebook.md), [Twitter](twitter.md) and [YouTube](youtube.md) and also skyrocketing popularity of online and massively online games, owing a lot to the gigantic success of [World of Warcraft](wow.md); all of these contributed to making Internet and computers one of the most mainstream and lucrative things, ruining everything. Cell phones became a commonly owned item and after about 2005 so called "[smart](smart.md) phones" and other "smart" devices replaced them as a universal communication device capable of connecting to the Internet. Year 2010 seems to be the turning point beyond which societal decline accelerated immensely; 1990s seem to have been the peak of society, after the year 2000 society started to slowly decline but by inertia things were still relatively good for about another decade. In 2011 [Minecraft](minecraft.md) was released. After this we've seen the rise of [Bitcoin](bitcoin.md) and other [cryptocurrencies](crypto.md). Before 2020 we've also seen a brief spike in popularity of [VR](vr.md) (that would diminish again) and a huge advancement in [neural network](neural_network.md) [Artificial Intelligence](ai.md) which will likely be the topic of the future. [Quantum computers](quantum.md) are being highly researched with already existing primitive prototypes; this will also likely be very important in the following years. Besides AI there were also [drones](drone.md), electromobiles, robotic Mars exploration and other things. However the society and technology have been in decadence for some time now, [capitalism](capitalism.md) has pushed technology to become hostile and highly [abusive to users](capitalist_software.md), extreme [bloat](bloat.md) of technology causes highly inefficient, extremely expensive and unreliable technology. In addition society is dealing with a lot of serious issues such as the [global warming](global_warming.md) and many people are foreseeing a [collapse of society](collapse.md).
After this very recent history follows, it's hard to judge which recent events will be of historical significance much later. 1990s have seen a huge growth of computer power, video [games](game.md) such as [Doom](doom.md) led to development of [GPU](gpu.md)s and high quality computer graphics along with a wide adoption of computers by common people, which in turn helped the further growth of Internet. In around mid 90s the [web](www.md) overtook [gopher](gopher.md) in popularity and started to become the forefront of the Internet. Late 90s saw the rise of the ["open source" movement](open_source.md) ([OSI](osi.md) was established in 1998). Worthy of mention is also the first animal cloned from an adult cell, sheep named Dolly, in 1996. In 1997 computer first beat human world [chess](chess.md) champion, it was the famous Kasparov vs [Deep Blue](deep_blue.md) match. Year 2000 was infamously preceded by the [Y2K](y2k.md) hysteria, the [fear](fear_culture.md) of technological [collapse](collapse.md) that was to be caused by computers flipping from year 99 to 00 -- this of course didn't happen. Shortly after 2000 [Lawrence Lessig](lessig.md) founded [Creative Commons](creative_commons.md), an organization that came hand in hand with the [free culture](free_culture.md) movement inspired by the [free software movement](free_software.md). At this point over 50% of US households had a computer. In 2003 the whole human [DNA](dna.md) was sequenced after 13 years of international collaborative effort. From 2005 we've seen a boom of [social networks](social_net.md) like [Facebook](facebook.md), [Twitter](twitter.md) and [YouTube](youtube.md) and also skyrocketing popularity of online and massively online games, owing a lot to the gigantic success of [World of Warcraft](wow.md); all of these contributed to making Internet and computers one of the most mainstream and lucrative things, ruining everything. Cell phones became a commonly owned item and after about 2005 so called "[smart](smart.md) phones" and other "smart" devices replaced them as a universal communication device capable of connecting to the Internet. Year 2010 seems to be the turning point beyond which societal decline accelerated immensely; 1990s seem to have been the peak of society, after the year 2000 society started to slowly decline but by inertia things were still relatively good for about another decade. In 2011 [Minecraft](minecraft.md) was released. After this we've seen the rise of [Bitcoin](bitcoin.md) and other [cryptocurrencies](crypto.md). Before 2020 we've also seen a brief spike in popularity of [VR](vr.md) (that would diminish again) and a huge advancement in [neural network](neural_network.md) [Artificial Intelligence](ai.md) which will likely be the topic of the future. 2022 saw the release of [ChatGPT](chatgpt.md), the AI chatbot that made a worldwide sensation by its human-like nature and intelligence -- the event will likely be seen as the moment of transition to a truly human-like AI. [Quantum computers](quantum.md) are being highly researched with already existing primitive prototypes; this will also likely be very important in the following years. Besides AI there were also [drones](drone.md), electromobiles, robotic Mars exploration and other things. However the society and technology have been in decadence for some time now, [capitalism](capitalism.md) has pushed technology to become hostile and highly [abusive to users](capitalist_software.md), extreme [bloat](bloat.md) of technology causes highly inefficient, extremely expensive and unreliable technology. In addition society is dealing with a lot of serious issues such as the [global warming](global_warming.md) and many people are foreseeing a [collapse of society](collapse.md).
Less [retarded](retard.md) society (LRS, same [acronym](acronym.md) as [less retarded software](lrs.md)) is a model of ideal society towards which we, the [LRS](lrs.md), want to be moving. Less retarded society is a peaceful, collaborative society based on [love](love.md) of all [life](life.md), which aims for maximum well being of all living beings, a society without violence, [money](money.md), oppression, need for [work](work.md), social [competition](competition.md), poverty, scarcity, criminality, [censorship](censorship.md), [self-interest](self_interest.md), government, police, laws, bullshit, slavery and many other negative phenomena. It equally values all living beings and establishes true social equality in which everyone can pursue his true desires freely -- it is a TRULY [leftist](left_vs_right.md) society, NOT a [pseudoleftist](pseudoleft.md) one. The society works similarly to that described by the [Venus Project](venus_project.md) and various [anarchist](anarchism.md) theories (especially [anarcho pacifist](anpac.md) [communism](communism.md)), but it also takes good things from elsewhere, even various [religions](religion.md) (without itself actually becoming a religion in traditional sense); for example parts of teaching of [Jesus](jesus.md) and [Buddha](buddhism.md).
Less [retarded](retard.md) society (LRS, same [acronym](acronym.md) as [less retarded software](lrs.md)) is a model of ideal society towards which we, the [LRS](lrs.md), want to be moving. Less retarded society is a [peaceful](pacifism.md), collaborative society based on [love](love.md) of all [life](life.md), which aims for maximum well being of all living beings, a society without violence, [money](money.md), oppression, need for [work](work.md), social [competition](competition.md), poverty, scarcity, criminality, [censorship](censorship.md), [self-interest](self_interest.md), [government](government.md), police, [laws](law.md), [bullshit](bullshit.md), slavery and many other negative phenomena. It equally values all living beings and establishes true social equality in which everyone can pursue his true desires freely -- it is a TRULY [leftist](left_vs_right.md) society, NOT a [pseudoleftist](pseudoleft.md) one. The society works similarly to that described by the [Venus Project](venus_project.md) and various [anarchist](anarchism.md) theories (especially [anarcho pacifist](anpac.md) [communism](communism.md)), but it also takes good things from elsewhere, even various [religions](religion.md) (without itself actually becoming a religion in traditional sense); for example parts of teaching of [Jesus](jesus.md) and [Buddha](buddhism.md).
**How is this different from other ideologies and "life philosophies"?** Well, one principal difference is that LRS doesn't want to [fight](fight_culture.md), in fact LRS adopts a **[pessimistic](pessimism.md), [defeatist](defeatism.md) mindset** to not compromise morality by any desire to "win the game", behaving correctly is more important than achieving a goal, ends do NOT justify the means; nowadays as well as in the past society has always been about conflict, playing a **game** against others (nowadays e.g. market competition, employment competition, media competition, ...) in which some win, some can manage and some lose. Most political parties nowadays just want to change the rules of the game or downright switch to a different kind of game, some want to make the rules "more fair", or to make it favor their represented minority (so called [fascism](fascism.md)), some just want to [hack](hacking.md) the game, some want to [cheat](cheat.md) to win the game easily, some want to play fair but still win (i.e. become "successful"). LRS simply sees any kind of such game as unnecessary, cruel, unethical and harmful in many ways not just to us, but to the whole planet. LRS therefore simply wants to stop the game, not by force but by making everyone see how bad the game is. It says that **competition and conflict must seize to be the basis of society**. There is no value in achieving anything by violence, such a change will soon be reverted by counter revolution, people themselves have to understand what's good and choose it voluntarily. That is one of the reasons why we are **[pacifists](pacifism.md)** and **reject all violence**, only wanting to promote our ideas by [education](education.md). We accept we may not achieve our goals and we most certainly won't achieve anything during our lifetime and that gives us the freedom to behave truly morally. We try to **never be [proud](pride.md)** of anything, as pride leads to violence and fascism. We are also in many ways aligned with the ideals of **[cynicism](cynicism.md)**.
**How is this different from other ideologies and "life philosophies"?** Well, one principal difference is that LRS doesn't want to [fight](fight_culture.md), in fact LRS adopts a **[pessimistic](pessimism.md), [defeatist](defeatism.md) mindset** to not compromise [morality](morality.md) by any desire to "win the game", behaving correctly is more important than achieving a goal, ends do NOT justify the means; nowadays as well as in the past society has always been about conflict, playing a **game** against others (nowadays e.g. market competition, employment competition, media competition, ...) in which some win, some can manage and some lose. Most political parties nowadays just want to change the rules of the game or downright switch to a different kind of game, some want to make the rules "more fair", or to make it favor their represented minority (so called [fascism](fascism.md)), some just want to [hack](hacking.md) the game, some want to [cheat](cheat.md) to win the game easily, some want to play fair but still win (i.e. become "successful"). LRS simply sees any kind of such game as unnecessary, cruel, unethical and harmful in many ways not just to us, but to the whole planet. LRS therefore simply wants to stop the game, not by force but by making everyone see how bad the game is. It says that **competition and conflict must seize to be the basis of society**. There is no value in achieving anything by violence, such a change will soon be reverted by counter revolution, people themselves have to understand what's good and choose it voluntarily. That is one of the reasons why we are **[pacifists](pacifism.md)** and **reject all violence**, only wanting to promote our ideas by [education](education.md). We accept we may not achieve our goals and we most certainly won't achieve anything during our lifetime and that gives us the freedom to behave truly morally. We try to **never be [proud](pride.md)** of anything, as pride leads to violence and fascism. We are also in many ways aligned with the ideals of **[cynicism](cynicism.md)**.
Note that less retarded society is an ideal model, i.e. it can probably not be achieved 100% but it's something that gives us a direction and to which we can **get very close** with enough effort. We create an ideal theoretical model and then try to [approximate](approximation.md) it in reality, which is a [scientific](science.md) approach that is utilized almost everywhere: for example [mathematics](math.md) defines a perfect sphere and such a model is then useful in practice even if we cannot ever create a mathematically perfect sphere in the real physical world -- the mathematical equations of a sphere guide us so that with enough effort we are able to create physical spheres that are pretty close to an ideal sphere. The same can be done with society. This largely refutes the often given argument that *"it's impossible to achieve so we shouldn't try at all"* -- we should try our best and the closer to the ideal we get, the better for us.
Micro$soft (officially Microsoft, MS) is a terrorist organization, [software](software.md) [corporation](corporation.md) named after [its founder](bill_gates.md)'s dick -- it is, along with [Google](google.md), [Apple](apple.md) [et al](et_al.md) one of the biggest organized crime groups in history, best known for holding the world captive with its highly abusive "[operating system](os.md)" called [Windows](windows.md), as well as for leading an aggressive war on [free software](free_software.md) and utilizing many unethical and/or illegal business practices such as destroying any potential competition with the [*Embrace Extend Extinguish*](eee.md) (actual terminology internally used at Microsoft) strategy or lately practicing heavy [openwashing](openwashing.md).
Micro$soft (officially Microsoft, MS) is a terrorist organization, [software](software.md) [corporation](corporation.md) named after [its founder](bill_gates.md)'s dick -- it is, along with [Google](google.md), [Apple](apple.md) [et al](et_al.md) one of the biggest organized crime groups in history, best known for holding the world hostage with its highly abusive "[operating system](os.md)" called [Windows](windows.md), as well as for leading an aggressive war on [free software](free_software.md) and utilizing many unethical and/or illegal business practices such as destroying any potential competition with the [*Embrace Extend Extinguish*](eee.md) (actual terminology internally used at Microsoft) strategy or lately practicing heavy [openwashing](openwashing.md).
{ [Techrights](techrights.md) documents Microsoft nicely on their wiki, see e.g. "Microsoft sins" at http://techrights.org/wiki/List_of_Microsoft_Sins, which among others list illegally shooting an antelope, tax evasion, attacking (physically and verbally) employees who leave for other companies and bribing bloggers to write positive reviews. ~drummyfish }
@ -8,7 +8,7 @@ Modern technology is also opposed by [neoluddists](neoluddism.md), a kind of ant
Sometimes random people notice the issue, though there are very few. One blog (https://blog.ari.lt/b/modernism/) for example goes on to say that "modernism sucks" and the word *modern* is basically just an excuse for being [bloated](bloat.md). Those are indeed true words.
**Avoid anything labeled as follows**: "modern", "state-of-the-art", "cutting-edge", "for 21st century", "for INSERT CURRENT YEAR", "up-to-date", "innovative", "novel", "latest technology", "high tech" etc.
**Avoid anything labeled as follows**: "modern", "state-of-the-art", "cutting-edge", "for 21st century", next gen, "for INSERT CURRENT YEAR", "up-to-date", "innovative", "novel", "latest technology", "high tech" etc.
Remember, [older is always better](older_is_better.md).
@ -127,8 +127,8 @@ Here patterns start to show, for example the level one of the tree are all prime
There are different types of numbers, in mathematics we classify them into [sets](set.md) (if we further also consider the operations we can perform with numbers we also sort them into algebras and structures like [groups](group.md), [fields](field.md) or [rings](ring.md)). Though we can talk about finite sets of numbers perfectly well (e.g. [modulo](mod.md) arithmetic, [Boolean algebra](boolean_algebra.md) etc.), we are firstly considering [infinite](infinity.md) sets (curiously some of these infinite sets can still be considered "bigger" than other infinite sets, e.g. by certain logic there is more real numbers than rational numbers, i.e. "fractions"). Some of these sets are subsets of others, some overlap and so forth. Here are some notable number sets (note that a list can potentially not capture all relationships between the sets):
- **all**: Anything conceivable as a number, even by stretch. E.g. [zero](zero.md), minus [infinity](infinity.md) or aleph one.
- **[noncomputable](computability.md)**: Cannot be computed, i.e. any such number has no [Turing machine](turing_machine.md) which when passed *N* on input would output *N*th digit of the number in finite time. E.g. Chaitin's constant (probability that a randomly generated program will halt).
- **[unknowable](knowability.md)**: Cannot be known for some reason, e.g. being non-computable or requiring more energy for their computation than will ever be present in our [Universe](universe.md).
- **[noncomputable](computability.md)**: Cannot be computed, i.e. any such number has no [Turing machine](turing_machine.md) which when passed *N* on input would output *N*th digit of the number in finite time. E.g. Chaitin's constant (probability that a randomly generated program will halt).
- **[transfinite (infinite) numbers](transfinite_number.md)**: Numbers that are in a sense "infinite", used to compare objects that are infinite in size (e.g. number sets themselves). E.g. omega, beth two or aleph one.
- **[surreal numbers](surreal_number.md)**, **\*R: hyperreal numbers**, **superreal numbers**, ...: Various extensions of real numbers, include also infinitesimals and some transfinite numbers.
- **[infinitesimals](infinitesimal.md)**: Are closer to zero than any real number without actually being zero, i.e. "infinitely small" numbers, play big role in [calculus](calculus.md). E.g. 0.000...1 (with infinitely many 0 digits before the 1).
@ -138,7 +138,7 @@ There are different types of numbers, in mathematics we classify them into [sets
- **complex integers**: Complex numbers with both real and imaginary component being integer. E.g. 13 - 2i, 44i or 0.
- **[algebraic](algebraic_number.md)**: Are roots of one variable [polynomials](polynomial.md) with integer coefficients. E.g. 4/3, the [golden ratio](golden_ratio.md) or square root of two.
- **[transcendental](transcendental_number.md)**: Aren't algebraic. E.g. [pi](pi.md), [sine](sin.md) of [e](e.md) or two to the power of square root of two.
- **[imaginary](imaginary_number.md)**: Have the same properties as real numbers but lie in another dimension, on a line perpendicular to the real number line, going through 0 -- they are connected to real numbers by the fact that imaginary unit ([i](i.md)) squared equals minus one. E.g. 0, 3i or -i.
- **[imaginary](imaginary_number.md)**: Are similar to real numbers but lie in another dimension, on a line perpendicular to the real number line, going through 0 -- they are connected to real numbers by the fact that imaginary unit ([i](i.md)) squared equals minus one. E.g. 0, 3i or -i.
- **R: [real](real_number.md)**: Measure any continuous one dimensional quantity (such as height or length), the line they form is continuous. E.g. -0.3, [pi](pi.md) or cube root of 10000.
- **negative**: Smaller than zero. E.g. -1, -123 or -1000.
- **R0+: non-negative**: Aren't negative. E.g. 0, 1 or 1000.
@ -165,7 +165,7 @@ Of course there are countless other number sets, especially those induced by var
There is a famous [encyclopedia](encyclopedia.md) of integer sequences at https://oeis.org/, made by number theorists -- it's quite [minimalist](minimalism.md), now also [free licensed](free_culture.md) (used to be [proprietary](proprietary.md), they seem to enjoy license hopping). At the moment it contains more than 370000 sequences; by browsing it you can get a glimpse of how deep the study of numbers goes. These people are also [funny](fun.md), they give numbers entertaining names like *happy numbers* (adding its squared digits eventually gives 1), *polite numbers*, *friendly numbers*, *cake numbers*, *lucky numbers* or *weird numbers*.
**Some numbers cannot be computed**, i.e. there exist [noncomputable](computability.md) numbers. This follows from the existence of noncomputable functions (such as that representing the [halting problem](halting_problem.md)). For example let's say we have a real number *x*, written in binary as *0. d0 d1 d2 d3 ...*, where *dn* is *n*th digit (1 or 0) after the radix point. We can define the number so that *dn* is 1 if and only if a [Turing machine](turing_machine.md) represented by number *n* halts. Number *x* is noncomputable because to compute the digits to any arbitrary precision would require being able to solve the unsolvable halting problem.
**Some numbers cannot be computed**, i.e. there exist [noncomputable](computability.md) numbers. This follows from the existence of noncomputable functions (such as that representing the [halting problem](halting_problem.md)). For example let's say we have a real number *x*, written in [binary](binary.md) as *0. d0 d1 d2 d3 ...*, where *dn* is *n*th digit (1 or 0) after the radix point. We can define the number so that *dn* is 1 if and only if a [Turing machine](turing_machine.md) represented by number *n* halts. Number *x* is noncomputable because to compute the digits to any arbitrary precision would require being able to solve the unsolvable halting problem.
**All [natural numbers](natural_number.md) are [interesting](interesting.md)**: there is a [fun](fun.md) [proof](proof.md) by contradiction of this. Suppose there exists a set of uninteresting numbers which is a subset of natural numbers; then the smallest of these numbers is interesting by being the smallest uninteresting number -- we've arrived at contradiction, therefore a set of uninteresting numbers cannot exist.
Real numbers are all [numbers](number.md) found on the infinite, continuous one dimensional number line, they often represent what we generally just mean by the term "number" and include for example [zero](zero.md), [pi](pi.md) or -39/11. The [set](set.md) or real numbers includes all [whole numbers](integer.md) as well as all [rational numbers](rational_number.md) (fractions with integer nominator and denominator), but in addition contains infinitely many "special" numbers such as [pi](pi.md), [e](e.md) or [square root](sqrt.md) of 2, numbers that are mathematically very interesting because they for example produce infinitely many digits in our traditional number notation without showing any obvious patterns. However it has to be noted real numbers still do NOT include for example [infinity](infinity.md) or [complex numbers](complex_number.md) (kind of "2D extension" of real numbers) such as [i](i.md). Real numbers really represent a **[continuum](continous.md)**, between any two numbers that are not the same there is always infinitely many real numbers that have no gaps in between -- this leads to the fact that not only is there infinitely many real numbers, but there is **[uncountably many](uncountable.md)** of them, i.e. simply put there is "more than traditional infinity" of real numbers. [Mathematically](math.md) the set of real numbers and operations with them form a structure called a *[field](field.md)* (so you'll often hear the term "field of real numbers").
WATCH OUT: even though in programming we sometimes we encounter [data types](data_type.md) named *real*, they usually don't represent true real numbers! In [programming](programming.md) we mostly only [approximate](approximation.md) real numbers with [floating](float.md) or [fixed](fixed_point.md) point numbers, which really are only rational numbers -- this is practically always [good enough](good_enough.md), we don't ever need an exact value of pi, a few decimal digits of accuracy is enough to an engineer, but to a mathematician real numbers represent a completely new, different world with some fundamental differences, which even a mere programmer should be at least aware of. Real numbers are tied to questions of the continuum, infinitely big and infinitely small, and they can really eventually lead to deep philosophical debates.
WATCH OUT: even though in programming we sometimes encounter [data types](data_type.md) named *real*, they usually don't represent true real numbers! In [programming](programming.md) we mostly only [approximate](approximation.md) real numbers with [floating](float.md) or [fixed](fixed_point.md) point numbers, which really are only rational numbers -- this is practically always [good enough](good_enough.md), we don't ever need an exact value of pi, a few decimal digits of accuracy is enough to an engineer, but to a mathematician real numbers represent a completely new, different world with some fundamental differences, which even a mere programmer should be at least aware of. Real numbers are tied to questions of the continuum, infinitely big and infinitely small, and they can really eventually lead to deep philosophical debates.
