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Learn why division by zero is a problematic special case in mathematics and computing. Explore different interpretations, definitions, and number systems of division by zero, and their implications for limits, functions, and errors.
Learn about the basic operation of division, its properties, notation, and generalizations to various algebraic structures. Find out how to divide natural numbers, integers, rational numbers, and real numbers, and what are the remainders and quotients.
A multiplicative inverse or reciprocal for a number x is a number which when multiplied by x yields 1. Learn the definition, examples, properties and applications of multiplicative inverses in different mathematical domains and contexts.
Learn about the meaning and use of division by infinity in mathematics, technology and calculus. Find out how different mathematical structures and methods handle this concept and what are the challenges and limitations of dividing by infinity.
The Collatz conjecture is a famous unsolved problem in mathematics that asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. Learn about the history, statement, proof attempts, and popular culture references of this conjecture.
Modulo is a mathematical operation that returns the remainder of a division. In computing, different systems and languages have different definitions and implementations of modulo, depending on the signs and types of the operands.
Indeterminate form is a term in calculus for certain limits that cannot be computed by taking the limits of each function separately. Learn about the types, examples, and methods of evaluating indeterminate forms, such as L'Hôpital's rule and equivalent infinitesimals.
Euler's identity is the equality where e is Euler's number, i is the imaginary unit, and π is pi. It is a special case of Euler's formula and a connection between five fundamental constants. Learn about its mathematical beauty, explanations, and applications.