In the context of solving equations, particularly in algebra and calculus, the terms "extraneous solutions" and "missing solutions" refer to specific types of solutions that can arise during the solving process. ### Extraneous Solutions Extraneous solutions are solutions that do not satisfy the original equation, even though they may appear to be valid solutions of the equation after manipulation. This often occurs when both sides of an equation are manipulated in a way that introduces solutions that do not work in the original equation.
This is the most important technical tutorial project that Ciro Santilli has done in his life so far as of 2019.
The scope is insane and unprecedented, and goes beyond Linux kernel-land alone, which is where it started.
It ended up eating every system programming content Ciro had previously written! Including:
so that that repo would better be called "System Programming Cheat". But "Linux Kernel Module Cheat" sounds more hardcore ;-)
Other major things that could be added there as well in the future are:
- github.com/cirosantilli/algorithm-cheat
- computer architecture tutorials with gem5
Due to this project, some have considered Ciro to be (archive):which made Ciro smile, although "Linux kernel documenter God" would have been more precise.
some kind of Linux kernel god.
[ 1.451857] input: AT Translated Set 2 keyboard as /devices/platform/i8042/s1│loading @0xffffffffc0000000: ../kernel_modules-1.0//timer.ko
[ 1.454310] ledtrig-cpu: registered to indicate activity on CPUs │(gdb) b lkmc_timer_callback
[ 1.455621] usbcore: registered new interface driver usbhid │Breakpoint 1 at 0xffffffffc0000000: file /home/ciro/bak/git/linux-kernel-module
[ 1.455811] usbhid: USB HID core driver │-cheat/out/x86_64/buildroot/build/kernel_modules-1.0/./timer.c, line 28.
[ 1.462044] NET: Registered protocol family 10 │(gdb) c
[ 1.467911] Segment Routing with IPv6 │Continuing.
[ 1.468407] sit: IPv6, IPv4 and MPLS over IPv4 tunneling driver │
[ 1.470859] NET: Registered protocol family 17 │Breakpoint 1, lkmc_timer_callback (data=0xffffffffc0002000 <mytimer>)
[ 1.472017] 9pnet: Installing 9P2000 support │ at /linux-kernel-module-cheat//out/x86_64/buildroot/build/
[ 1.475461] sched_clock: Marking stable (1473574872, 0)->(1554017593, -80442)│kernel_modules-1.0/./timer.c:28
[ 1.479419] ALSA device list: │28 {
[ 1.479567] No soundcards found. │(gdb) c
[ 1.619187] ata2.00: ATAPI: QEMU DVD-ROM, 2.5+, max UDMA/100 │Continuing.
[ 1.622954] ata2.00: configured for MWDMA2 │
[ 1.644048] scsi 1:0:0:0: CD-ROM QEMU QEMU DVD-ROM 2.5+ P5│Breakpoint 1, lkmc_timer_callback (data=0xffffffffc0002000 <mytimer>)
[ 1.741966] tsc: Refined TSC clocksource calibration: 2904.010 MHz │ at /linux-kernel-module-cheat//out/x86_64/buildroot/build/
[ 1.742796] clocksource: tsc: mask: 0xffffffffffffffff max_cycles: 0x29dc0f4s│kernel_modules-1.0/./timer.c:28
[ 1.743648] clocksource: Switched to clocksource tsc │28 {
[ 2.072945] input: ImExPS/2 Generic Explorer Mouse as /devices/platform/i8043│(gdb) bt
[ 2.078641] EXT4-fs (vda): couldn't mount as ext3 due to feature incompatibis│#0 lkmc_timer_callback (data=0xffffffffc0002000 <mytimer>)
[ 2.080350] EXT4-fs (vda): mounting ext2 file system using the ext4 subsystem│ at /linux-kernel-module-cheat//out/x86_64/buildroot/build/
[ 2.088978] EXT4-fs (vda): mounted filesystem without journal. Opts: (null) │kernel_modules-1.0/./timer.c:28
[ 2.089872] VFS: Mounted root (ext2 filesystem) readonly on device 254:0. │#1 0xffffffff810ab494 in call_timer_fn (timer=0xffffffffc0002000 <mytimer>,
[ 2.097168] devtmpfs: mounted │ fn=0xffffffffc0000000 <lkmc_timer_callback>) at kernel/time/timer.c:1326
[ 2.126472] Freeing unused kernel memory: 1264K │#2 0xffffffff810ab71f in expire_timers (head=<optimized out>,
[ 2.126706] Write protecting the kernel read-only data: 16384k │ base=<optimized out>) at kernel/time/timer.c:1363
[ 2.129388] Freeing unused kernel memory: 2024K │#3 __run_timers (base=<optimized out>) at kernel/time/timer.c:1666
[ 2.139370] Freeing unused kernel memory: 1284K │#4 run_timer_softirq (h=<optimized out>) at kernel/time/timer.c:1692
[ 2.246231] EXT4-fs (vda): warning: mounting unchecked fs, running e2fsck isd│#5 0xffffffff81a000cc in __do_softirq () at kernel/softirq.c:285
[ 2.259574] EXT4-fs (vda): re-mounted. Opts: block_validity,barrier,user_xatr│#6 0xffffffff810577cc in invoke_softirq () at kernel/softirq.c:365
hello S98 │#7 irq_exit () at kernel/softirq.c:405
│#8 0xffffffff818021ba in exiting_irq () at ./arch/x86/include/asm/apic.h:541
Apr 15 23:59:23 login[49]: root login on 'console' │#9 smp_apic_timer_interrupt (regs=<optimized out>)
hello /root/.profile │ at arch/x86/kernel/apic/apic.c:1052
# insmod /timer.ko │#10 0xffffffff8180190f in apic_timer_interrupt ()
[ 6.791945] timer: loading out-of-tree module taints kernel. │ at arch/x86/entry/entry_64.S:857
# [ 7.821621] 4294894248 │#11 0xffffffff82003df8 in init_thread_union ()
[ 8.851385] 4294894504 │#12 0x0000000000000000 in ?? ()
│(gdb)77K. Low enough for "high temperature superconductors" such as yttrium barium copper oxide, but for "low temperature superconductors", you need to go much lower, typically with liquid helium, which is likely much more expensive. TODO by how much?
Where Do You Get Liquid Nitrogen? by The King of Random (2016)
Source. He just goes to a medical gases shop in a local industrial estate and buys 20L for 95 dollars and brings it back on his own Dewar marked 35LD.Making Liquid Nitrogen From Scratch! by Veritasium (2019)
Source. "From scratch" is perhaps a bit clickbaity, but I'll take it.Factorization is the process of breaking down an expression, number, or polynomial into a product of its factors. Factors are numbers or expressions that can be multiplied together to obtain the original number or expression. Factorization is a fundamental concept in mathematics, used in various areas such as arithmetic, algebra, and number theory.
The term "formula" can have different meanings depending on the context in which it is used: 1. **Mathematics and Science**: In mathematics and science, a formula is a concise way of expressing information symbolically. It consists of mathematical symbols and numbers that represent a relationship or rule.
Division is one of the four basic arithmetic operations in mathematics, alongside addition, subtraction, and multiplication. It involves splitting a number into equal parts or groups. The primary components of a division operation are: - **Dividend**: The number that is being divided. - **Divisor**: The number by which the dividend is divided. - **Quotient**: The result of the division.
A linear equation is a mathematical equation that represents a straight line when graphed on a coordinate plane. It typically takes the form: \[ ax + by + c = 0 \] or in slope-intercept form: \[ y = mx + b \] where: - \( x \) and \( y \) are the variables. - \( a \), \( b \), and \( c \) are constants (with \( a \) and \( b \) not both zero).
List of High-temperature superconductors by 
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01Rationalization in mathematics is the process of eliminating irrational numbers (such as square roots or cube roots) from the denominator of a fraction. This is done to simplify mathematical expressions and make them easier to work with.
List of personal knowledge base software by Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01Lists:
- www.bibsonomy.org/user/bshanks/education fantastic list, presumably by this guy:
- www.reddit.com/r/Zettelkasten/comments/168cmca/which_note_taking_app_for_a_luhmann_zettlekasten/
- www.reddit.com/r/productivity/comments/18vvavl/best_free_notetaking_app_switching_from_evernote/
- github.com/topics/note-taking has a billion projects. Oops.
- www.noteapps.ca/
Personal knowledge base recommendation threads:
TODO look into those more:
- roamresearch.com/ no public graphs
- nesslabs.com/roam-research-alternatives a bunch of open source alternatives to it
- Trillium Notes. Notable project! Pun unintended!
- Stroll giffmex.org/stroll/stroll.html. How to publish? How to see tree?
- tiddlyroam joekroese.github.io/tiddlyroam/ graph rather than text searchable ToC. Public instance? Multiuser?
- Athens github.com/athensresearch/athens rudimentary WYSIWYG
- Logseq github.com/logseq/logseq no web interface/centralized server?
- itsfoss.com/obsidian-markdown-editor. Closed source. They have an OK static website publication mechanism: publish.obsidian.md/ram-rachum-research/Public/Agents+aren't+objective+entities%2C+they're+a+model but leaf node view only for now, no cross source page render. They are committed to having plaintext source which is cool: twitter.com/kepano/status/1675626836821409792
- CherryTree github.com/giuspen/cherrytree written in C++, GTK, WYSIWYG
- github.com/dullage/flatnotes: Python
- github.com/usememos/memos: Go
- github.com/siyuan-note/siyuan: Go
- github.com/vnotex/vnote: C++
- github.com/Laverna/laverna: JavaScript
- github.com/taniarascia/takenote
- github.com/silverbulletmd/silverbullet: TypeScript, Markdown, web-based WYSIWYG, focus on querying
Major downsides that most of those personal knowledge databases have:
- very little/no focus on public publishing, which is the primary focus of OurBigBook.com
- either limited or no multiuser features, e.g. edit protection and cross user topics
- graph based instead of tree based. For books we need a single clear ordering of a tree. Graph should come as a secondary thing through tags.
Closed source dump:
- www.toodledo.com
- Simplenote: en.wikipedia.org/wiki/Simplenote, by WordPress.com operator company Automattic
Solving quadratic equations using continued fractions is a method linked to the approximation of the solutions of these equations through the use of continued fractions. Quadratic equations typically take the form: \[ ax^2 + bx + c = 0 \] where \(a\), \(b\), and \(c\) are coefficients, and \(x\) is the variable we want to solve for.
Loop-mediated isothermal amplification by Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01Like PCR, but does not require thermal cycling. Thus the "isothermal" in the name: iso means same, so "same temperature".
Not needing the thermo cycling means that the equipment needed is much smaller and cheaper it seems.
Lorentz transform consequence: everyone sees the same speed of light by Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01OK, so let's verify the main desired consequence of the Lorentz transformation: that everyone observes the same speed of light.
Observers will measure the speed of light by calculating how long it takes the light going towards cross a rod of length laid in the x axis at position .
Each observer will observe two events:
Supposing that the standing observer measures the speed of light as and that light hits the left side of the rod at time , then he observes the coordinates:
Now, if we transform for the moving observer:and so the moving observer measures the speed of light as:
Two-element Boolean algebra, also known as Boolean algebra of two values, is a mathematical structure that deals with binary variables that can take on one of two values: typically represented as 0 and 1. This framework is foundational to digital logic and computer science.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact