1×0

1×0 denotes the product of the integers 1 and 0. In standard arithmetic this equals 0, a result that follows from the zero property of multiplication: any number multiplied by zero yields zero. Because 1 is the multiplicative identity, 1×a = a for any a, but when a is 0 the result is 0. Interpreted as repeated addition, 1×0 is the sum of 1 added to itself zero times, which also yields 0.

The expression is often cited to illustrate basic arithmetic laws. It is commutative, so 1×0 = 0×1, and it participates in the associative and distributive properties that govern multiplication over addition and other operations.

Beyond plain numbers, 1×0 can be interpreted in other mathematical contexts. In set theory, the Cartesian product A×B has cardinality |A|×|B|; if |A| = 1 and |B| = 0, then A×B is the empty set with cardinality zero. In linear algebra and matrix theory, a 1×0 matrix is a matrix with one row and zero columns, an object sometimes used to represent degenerate or empty structures. Such a matrix can participate in larger matrix products, for example connecting with compatible-dimension multiplications that yield a meaningful result.

In applied contexts, 1×0 appears in programming, algorithms, and computer science as a concrete example of a product that yields zero, reinforcing the general principle that multiplying by zero resets a quantity to zero. Overall, 1×0 is a simple yet foundational instance used to illustrate rules of multiplication and the behavior of zero in arithmetic.