"Singly even" and "doubly even" typically refer to types of numbers in the context of mathematics, particularly in discussing properties of integers or sets of integers. 1. **Singly Even Numbers**: A number is termed "singly even" if it is divisible by 2 but not by 4. In other words, singly even numbers can be expressed in the form \(4k + 2\), where \(k\) is an integer.

A sparsely totient number is a positive integer \( n \) for which the ratio of the Euler's totient function \( \varphi(n) \) to \( n \) is relatively small compared to other integers. More formally, a number \( n \) is considered a sparsely totient number if: \[ \frac{\varphi(n)}{n} < \frac{1}{\log n} \] for sufficiently large \( n \).

A sphenic number is a positive integer that is the product of three distinct prime numbers. In other words, a sphenic number can be expressed in the form \( p_1 \times p_2 \times p_3 \), where \( p_1 \), \( p_2 \), and \( p_3 \) are prime numbers and \( p_1 \), \( p_2 \), and \( p_3 \) are all different from one another.

A Størmer number is a specific type of number in number theory that is associated with the properties of the prime factorization of positive integers. It is defined by the following property: A positive integer \( n \) is called a Størmer number if it is equal to the sum of the digits in its prime factorization, each counted with multiplicity.

The term "superfactorial" is used to refer to an extension of the factorial function, similar to how tetration is an extension of exponentiation. The superfactorial of a positive integer \( n \) is denoted as \( \text{sf}(n) \) and is defined as the product of the factorials of all positive integers up to \( n \). Mathematically, it is defined as: \[ \text{sf}(n) = 1!

A Thabit number is a specific type of integer that is part of a mathematical sequence defined by certain properties. The Thabit numbers are related to the Fibonacci sequence, specifically by being represented as a summation involving Fibonacci numbers. Formally, the n-th Thabit number \( T_n \) can be defined as: \[ T_n = \sum_{k=1}^{n} F_k \] where \( F_k \) denotes the k-th Fibonacci number.

Zero (0) is a number that represents a null quantity or the absence of value. It serves several important roles in mathematics and various number systems. Here are some key aspects of zero: 1. **Identity Element**: In addition, zero is the additive identity, meaning that when you add zero to any number, the value of that number remains unchanged (e.g., \(x + 0 = x\)).

The number 1 is a basic numerical value that represents a single unit or a single whole. It is the first positive integer and is often used as a foundational element in mathematics. In various contexts, 1 can denote unity, identity, or singularity. For example: - In arithmetic, it is the multiplicative identity, meaning any number multiplied by 1 remains unchanged. - In set theory, a set with one element has a cardinality of 1.

1,000,000,000 is one billion. In numerical form, it is represented as 1 followed by nine zeros.

A quadratic integer is a type of algebraic integer that is a root of a monic polynomial of degree two with integer coefficients. In simpler terms, a quadratic integer can be expressed in the form \( a + b\sqrt{d} \), where \( a \) and \( b \) are integers, and \( d \) is a square-free integer (i.e., \( d \) is not divisible by the square of any prime).

Real transcendental numbers are a subset of real numbers that are not algebraic. An algebraic number is defined as any number that is a root of a non-zero polynomial equation with integer coefficients. In contrast, transcendental numbers are not solutions to any such polynomial equation. For example, both rational numbers (like \( \frac{1}{2} \)) and irrational numbers (like \(\sqrt{2}\)) are algebraic, as they can be roots of polynomial equations with integer coefficients.

An irrational number is a type of real number that cannot be expressed as a simple fraction or ratio of two integers. This means that if a number is irrational, it cannot be written in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). Irrational numbers have non-repeating, non-terminating decimal expansions. This means their decimal representations go on forever without repeating a pattern.

A "schizophrenic number" is not a widely recognized term in mathematics or any scientific discipline, and there doesn't appear to be a standard definition or concept associated with it in the literature. It may be a colloquial or niche term that does not have broad use or acceptance.

The fast-growing hierarchy is a classification of functions based on their growth rates, typically used in mathematical logic and proof theory. It is a way to organize functions that grow faster than any computable function, providing a deeper understanding of the limits of computation and the nature of large numbers. The hierarchy is constructed using specific operations and is related to the *Buchholz hierarchy*, an extension of the * ordinals*.

Indefinite and fictitious numbers refer to concepts in different mathematical contexts, though they aren't standard terms in a traditional mathematical sense. However, here’s a breakdown of how these terms can be understood: ### Indefinite Numbers Indefinite numbers may refer to numbers that are not fixed or clearly defined.

Pentation is a mathematical operation that is part of the family of hyperoperations, which extend beyond exponentiation. Hyperoperations are defined in a sequence where each operation is one rank higher than the previous one, starting from addition, multiplication, exponentiation, and moving on to tetration and beyond. The sequence is as follows: 1. Addition (a + b) 2. Multiplication (a × b) 3. Exponentiation (a^b) 4.

"The Sand Reckoner" is a mathematical treatise written by the ancient Greek philosopher and mathematician Archimedes. In this work, Archimedes explores the concept of large numbers and methods for counting them, demonstrating his ability to quantify sizes much larger than what was typically considered at the time.

The International Standard Book Number (ISBN) system assigns unique identifiers to books and similar media. Each ISBN is composed of several elements, one of which is the registration group identifier, which indicates the country, geographical area, or language community in which the book is published. Here is a brief overview of the main ISBN registration groups: 1. **0 or 1**: English-speaking countries (USA, Canada, UK, Australia) 2.

As of my last knowledge update in October 2021, there is no widely recognized term or entity known as "Binade." However, it's possible that "Binade" could refer to a range of things, such as a brand, product, or concept that has emerged since then.

Gujarati numerals are the numeral system used to represent numbers in the Gujarati language, which is spoken primarily in the Indian state of Gujarat. This numeral system is derived from the Indian numeral system and has distinct symbols for the digits 0 to 9.