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Division by zero

In mathematics, division by zero, division where the divisor (denominator) is zero, is a problematic special case. Using fraction notation, the general example can be written as ⁠ a 0 {\displaystyle {\tfrac {a}{0}}} ⁠, where ⁠ a {\displaystyle a} ⁠ is the dividend (numerator).

History & Standards

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Division by zero at a glance

The strongest research directions include Higher mathematics and Computer arithmetic. Use the connected concepts below as starting points, not as a keyword checklist.

IntegersRational numbersComplex numbersSet theoryPeano's axiom systemFloating-point arithmeticIEEE 754Significand

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Overview

Elementary arithmetic

Early attempts

Calculus

Alternative number systems

Higher mathematics

Computer arithmetic

Historical accidents

Sources

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Division by zero

Top relations

related to Further reading · 31
Division by zero → Alfred, Book, By Zero, Ch, Charles, Dangerous Idea, Deductive Sciences, Definitions, Division, Dover, Eugene, Five Approaches, Introduction, ISBN, Logic, Mathematics, Methodology, New York, Northrop, Oxford University Press
related to Higher mathematics · 9
Division by zero → Answering, As, During, For, In, Loosely, Similarly, The, Why
related to Integer arithmetic · 7
Division by zero → ARM, Because, CPUs, In, Integer, PowerPC, Python
related to Abstract algebra · 5
Division by zero → Adjoining, Furthermore, However, In, Nevertheless
related to Historical accidents · 5
Division by zero → CG-48, On, Remote Data Base Manager, September, USS Yorktown
related to Inverse of multiplication · 4
Division by zero → An, Division, However, Thus
related to Fallacies · 2
Division by zero → For, When
related to Non-standard analysis · 2
Division by zero → In, The

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Important terminology

displaystyle zero division number numbers tfrac infinity real infty undefined example function arithmetic quotient negative positive result limit multiplication value

Entity relationships Subject–Predicate–Object triples

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SubjectPredicateObjectConfidenceSrc
the real numbersinstance ofas the resulting limit depends on the specific functions forming the fraction and cannot be determined from their separate limits.As an alternative to the common convention of w…0.80text
leaving division by zero undefinedinstance ofas the resulting limit depends on the specific functions forming the fraction and cannot be determined from their separate limits.As an alternative to the common convention of w…0.80text
it is possible to define the result of division by zero in other waysinstance ofas the resulting limit depends on the specific functions forming the fraction and cannot be determined from their separate limits.As an alternative to the common convention of w…0.80text
resulting in different number systemsinstance ofas the resulting limit depends on the specific functions forming the fraction and cannot be determined from their separate limits.As an alternative to the common convention of w…0.80text
Peano's axiom systeminstance ofare established on an axiomatic basis0.80text
then this is expanded to the ring of integersinstance ofare established on an axiomatic basis0.80text
Division by zerorelated to Abstract algebraIn0.60section
Division by zerorelated to Abstract algebraAdjoining0.60section
Division by zerorelated to Abstract algebraHowever0.60section
Division by zerorelated to Abstract algebraNevertheless0.60section
Division by zerorelated to Abstract algebraFurthermore0.60section
Division by zerorelated to FallaciesWhen0.60section

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    Division by zero

    Nodes149
    Edges148
    Triples71
    Avg. degree1.99
    Density0.013423
    Components1
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