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Why properties are important?
Properties are the laws of Mathematics that state that a mathematician must follow these rules [the properties] to solve a math problem. Every math topic, such as Geometry and Algebra, follow these properties. A maths system that doesn't follow, for example, with the association property in: a • b = b • a is not, in simple terms, mathematics. Thus, it is essential for every mathematician to, not only memorize, but apply these properties as well.
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