Common · Knowledge
Zero-product property
Mathematical property shared by many number systems, that a product cannot be zero unless one of its factors is zero
In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, if a b = 0 , then a = 0 or b = 0. {\displaystyle {\text{if }}ab=0,{\text{ then }}a=0{\text{ or }}b=0.} This property is also known as the rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nonzero zero divisors, or one of the two zero-factor properties.
From Wikipedia
In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, if a b = 0 , then a = 0 or b = 0. {\displaystyle {\text{if }}ab=0,{\text{ then }}a=0{\text{ or }}b=0.} This property is also known as the rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nonzero zero divisors, or one of the two zero-factor properties. All of the number systems studied in elementary mathematics — the integers Z {\displaystyle \mathbb {Z} } , the rational numbers Q {\displaystyle \mathbb {Q} } , the real numbers R {\displaystyle \mathbb {R} } , and the complex numbers C {\displaystyle \mathbb {C} } — satisfy the zero-product property. In general, a ring which satisfies the zero-product property is called a domain.
Text: Wikipédia, CC BY-SA 4.0. ·
Related cards
-
★★★
Division by zero
The result yielded by a real number when divided by zero
-
★★★
Monomial
Polynomial which has only one term
-
★★★
Parity of zero
Quality of the number zero as either even or odd
-
R★★
Rational root theorem
Theorem
-
C★
Commensurability (mathematics)
When two functions have co-rational periods, i.e. n T1 = m T2
-
★
Sign (mathematics)
Number property of being positive or negative