The Lossy Counting Algorithm is a streaming algorithm designed for the estimation of frequency counts of items in a data stream. It's particularly useful when dealing with large volumes of data where it is impractical to store and count each individual element due to memory constraints. The primary goal of the Lossy Counting Algorithm is to maintain an approximate count of elements that may exceed a certain frequency threshold.
Mathematics by Ciro Santilli 40 Updated 2025-07-16
The proper precise definition of mathematics can be found at: Section "Formalization of mathematics".
The most beautiful things in mathematics are described at: Section "The beauty of mathematics".
Figure 1. . Source. Applies to almost all of mathematics of course. But we don't care, do we!
The Redundancy Theory of Truth is a philosophical position concerning the nature of truth, primarily associated with the work of philosophers such as Frank P. Ramsey and later developed by others like Paul Horwich. This theory asserts that the concept of truth is redundant and that the predicate "is true" does not add any new information to the propositions it is applied to. Instead, the theory claims that truth can be expressed by simply asserting the proposition itself.
EPNdB stands for "Equivalent Noise Power in Decibels." It is a metric used to quantify the noise performance of communication systems, particularly in the context of radio and telecommunications. EPNdB expresses the noise figure or noise performance in decibels, allowing for easier comparison of different systems or components. Essentially, EPNdB helps engineers and designers understand how much noise a device introduces relative to its signal.
In the context of mathematical and theoretical physics, a symmetric spectrum often refers to a situation where certain properties or quantities exhibit symmetry, leading to a balanced and uniform distribution or behavior. However, the term can have specific meanings depending on the field of study. 1. **In Mathematics (especially in Spectral Theory)**: A symmetric spectrum can refer to the eigenvalues of a symmetric operator or matrix, where spectral properties are analyzed for their symmetries.
Flexible displays refer to screen technologies that can be bent, rolled, or otherwise shaped without losing functionality. These displays are typically made with materials such as organic light-emitting diodes (OLEDs), electronic paper, or liquid crystal displays (LCDs) with flexible substrates.
A foot per second (ft/s or ft/sec) is a unit of speed or velocity that indicates how many feet are traveled in one second. It is part of the imperial system of measurement and is commonly used in the United States for various applications, including engineering, physics, and everyday life.
T-symmetry, or time reversal symmetry, is a concept in physics that refers to the invariance of the laws of physics under the reversal of the direction of time. In other words, a physical process is said to exhibit T-symmetry if the fundamental equations governing the dynamics of the system remain unchanged when the time variable is replaced by its negative (\(t \rightarrow -t\)).
A Tornado Debris Signature (TDS) is a specific pattern observed in radar data that indicates the presence of a tornado and the associated debris being lifted into the atmosphere. When a tornado occurs, it can pick up various materials from the ground, such as dirt, leaves, and man-made objects, and fling them into the air. This debris can create a distinct radar signature. Meteorologists use Doppler radar to detect these signatures during storm events.
Ukrainian biophysicists are scientists from Ukraine who specialize in the field of biophysics, which is an interdisciplinary area that combines principles from physics and biology to study biological systems. Biophysicists often focus on understanding the physical properties and behaviors of biological molecules, cells, and organisms, employing techniques from physics to explore complex biological processes.
A furlong is a unit of distance that is equal to one-eighth of a mile, or 220 yards, which is approximately 201.168 meters. The term comes from an Old English word meaning "furrow long," originally referring to the length of a furrow in a plowed field. It is primarily used in horse racing and in some agricultural contexts. In these settings, distances for races or fields are often measured in furlongs for tradition and practicality.
Bagh-Chal is a traditional board game that originates from Nepal. It is played between two players, where one takes on the role of the "tiger" and the other plays as the "goats." The objective for the tiger player is to capture all the goats, while the goat player aims to block the tiger's movements and protect their goats.
A consignee is the person or entity to whom goods are delivered or shipped. In the context of shipping and logistics, the consignee is typically the buyer or recipient of the goods. The role of the consignee can vary depending on the arrangement between the parties involved in the transaction. Key points about a consignee include: 1. **Recipient Role**: The consignee receives the goods from the consignor (the sender or seller) and is responsible for taking possession of them.
The Arrhenius equation is a formula used in chemistry to express the temperature dependence of reaction rates. It quantifies how the rate of a chemical reaction increases with an increase in temperature and is commonly represented in the following form: \[ k = A e^{-\frac{E_a}{RT}} \] Where: - \( k \) is the rate constant of the reaction.
Solar transit refers to the passage of the Sun across a particular point in the sky, or more specifically, its movement along the ecliptic plane as observed from Earth. This can manifest in different contexts: 1. **Astronomical Context**: In astronomy, solar transit can refer to the transit of the Sun across the local meridian, which is the highest point the Sun reaches in the sky at a given location (solar noon).
The Arf invariant is a topological invariant associated with a smooth, oriented manifold, particularly in the context of differential topology and algebraic topology. It is especially relevant in the study of 4-manifolds and can be used to classify certain types of manifolds. The Arf invariant can be defined for a non-singular quadratic form over the field of integers modulo 2 (denoted as \(\mathbb{Z}/2\mathbb{Z}\)).
Tidal bores are natural phenomena that occur in certain rivers and estuaries where a strong incoming tide creates a single wave or a series of waves that travel upstream against the river's current. This event happens when the tidal range is significant, and the shape of the river channel allows for the rapid accumulation of water.

Pinned article: 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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . 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.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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