2×0

2×0 denotes the product of the numbers 2 and 0 in standard arithmetic. In common number systems such as integers, rationals, reals, and complex numbers, the result is 0.

A simple interpretation is through repeated addition: multiplying 2 by 0 yields zero copies of 2, which is 0. More formally, in the familiar axioms of arithmetic, multiplication by zero is an absorbing property: for any number a, a×0 = 0 and 0×a = 0.

This property is a consequence of the distributive law: a×(b+ c) = a×b + a×c. If you set b = 0 and c = 0, you obtain a×0 = a×0 + a×0, which implies a×0 must equal 0. The same logic holds symmetrically for 0×a. Consequently, zero is the absorbing element for multiplication.

Generalizations and contexts: the statement 2×0 = 0 remains true in modular arithmetic as well, where calculations are taken modulo n. In any standard algebraic structure that defines multiplication (such as rings, fields, and modules with scalar multiplication), multiplying by the zero element yields zero. The identity element for addition is 0, and the multiplication by zero property is a fundamental aspect of its behavior across these systems.

In summary, 2×0 equals 0, a result that reflects the broader rule that any number or element multiplied by the zero element yields the zero element.

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