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roger
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What is the rigorous definition of multiplication and how can it be shown to be like repeated addition ?
matt grime said:The rigorous definition of multiplying positive integers is that it is repeatedly adding them.
It is extended to rationals algebraically, and to the reals by continuity, and thence the complexes by algebraic means.
See the VSI (A Very Short Introduction to) book on Mathematics.
? It is a subgroup! Or, rather, is isomorphic to a subgroup. Mapping {0, 1, 2} to {0, 9, 18}, in that order, is an isomorphism.roger said:but why isn't the set Z3,+ a subgroup of Z7,+ ?
Sorry. For some reason my eyes bollixed on me and I read Z7 as Z27!HallsofIvy said:? It is a subgroup! Or, rather, is isomorphic to a subgroup. Mapping {0, 1, 2} to {0, 9, 18}, in that order, is an isomorphism.
Multiplication is a mathematical operation that involves combining two or more numbers to find their total product. It is often represented by the symbol "x" or "*".
Multiplication is different from addition because it involves repeated addition. For example, 2 x 3 means adding 2 three times: 2 + 2 + 2 = 6. Addition, on the other hand, simply combines two or more numbers to find their total.
The basic rules of multiplication include the commutative property, which states that the order of the numbers does not affect the product (e.g. 2 x 3 = 3 x 2), and the associative property, which states that the grouping of numbers does not affect the product (e.g. 2 x 3 x 4 = (2 x 3) x 4 = 24).
Multiplication and division are inverse operations. This means that multiplication can be used to solve division problems (e.g. 6 / 3 = 6 x (1/3) = 2), and division can be used to solve multiplication problems (e.g. 2 x 3 = 6 ÷ 3 = 2).
Multiplication is used in everyday life for tasks such as calculating prices at the grocery store, determining the total number of items in a group, and finding the area or volume of a shape. It is also used in many fields of science, including physics, chemistry, and engineering.