Ana Sayfa
Matematikçiler
Makaleler
Matematik Seçkileri
Fraktallar
Paradokslar
Sayılar Teorisi
=> Algebraic Curves-Mordell Curve
=> Algebraic Curves-Ochoa Curve
=> Algebraic Integer
=> Algebraic Number
=> Algebraic Number Theory
=> Chebotarev Density Theorem
=> Class Field
=> Cyclotomic Field
=> Dedekind Ring
=> Fractional Ideal
=> Global Field
=> Local Field
=> Number Field Signature
=> Picard Group
=> Pisot Number
=> Weyl Sum
=> Casting Out Nines
=> A-Sequence
=> Anomalous Cancellation
=> Archimedes' Axiom
=> B2-Sequence
=> Calcus
=> Calkin-Wilf Tree
=> Egyptian Fraction
=> Egyptian Number
=> Erdős-Straus Conjecture
=> Erdős-Turán Conjecture
=> Eye of Horus Fraction
=> Farey Sequence
=> Ford Circle
=> Irreducible Fraction
=> Mediant
=> Minkowski's Question Mark Function
=> Pandigital Fraction
=> Reverse Polish Notation
=> Division by Zero
=> Infinite Product
=> Karatsuba Multiplication
=> Lattice Method
=> Pippenger Product
=> Reciprocal
=> Russian Multiplication
=> Solidus
=> Steffi Problem
=> Synthetic Division
=> Binary
=> Euler's Totient Rule
=> Goodstein Sequence
=> Hereditary Representation
=> Least Significant Bit
=> Midy's Theorem
=> Moser-de Bruijn Sequence
=> Negabinary
=> Negadecimal
=> Nialpdrome
=> Nonregular Number
=> Normal Number
=> One-Seventh Ellipse
=> Quaternary
=> Radix
=> Regular Number
=> Repeating Decimal
=> Saunders Graphic
=> Ternary
=> Unique Prime
=> Vigesimal
Ziyaretçi defteri
 

Division by Zero

Division by zero is the operation of taking the quotient of any number x and 0, i.e., x/0. The uniqueness of division breaks down when dividing by zero, since the product 0·y=0 is the same for any y, so y cannot be recovered by inverting the process of multiplication. 0 is the only number with this property and, as a result, division by zero is undefined for real numbers and can produce a fatal condition called a "division by zero error" in computer programs.

To the persistent but misguided reader who insists on asking "What happens if I do divide by zero," Derbyshire (2004, p. 36) provides the slightly flippant but firm and concise response, "You can't. It's against the rules." Even in fields other than the real numbers, division by zero is never allowed (Derbyshire 2004, p. 266).

There are, however, contexts in which division by zero can be considered as defined. For example, division by zero z/0 for z in C^*!=0 in the extended complex plane C-* is defined to be a quantity known as complex infinity. This definition expresses the fact that, for z!=0, lim_(w->0)z/w=infty (i.e., complex infinity). However, even though the formal statement 1/0=infty is permitted in C-*, note that this does not mean that 1=0·infty. Zero does not have a multiplicative inverse under any circumstances.

Although division by zero is not defined for reals, limits involving division by a real quantity x which approaches zero may in fact be well-defined. For example,

 lim_(x->0)(sinx)/x=1.

Of course, such limits may also approach infinity,

 lim_(x->0^+)1/x=infty.
 

Bugün 198 ziyaretçi (234 klik) kişi burdaydı!
Bu web sitesi ücretsiz olarak Bedava-Sitem.com ile oluşturulmuştur. Siz de kendi web sitenizi kurmak ister misiniz?
Ücretsiz kaydol