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Is there any situation in which the Distributive Law of Multiplication is false? For a specific concept, expression, whatever may it be. Is it safe to say that it will always be true, no matter the context?

Gabriel Silva
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  • It can be a property or axiom depending on your approach (see here). How do you define multiplication? – Golden_Ratio Feb 22 '22 at 00:51
  • Left distribution and Right distribution are two axioms of a ring. See the 3rd axiom of the definition of a Ring here: https://math.stackexchange.com/questions/513223/example-of-ring-without-the-distributive-property So for a structure without distribution, have a ring without the two distribution axioms. Although now the multiplication is not really the multiplication you are familiar with. So the short answer is no. – Adam Rubinson Feb 22 '22 at 00:54
  • related https://math.stackexchange.com/questions/1621842/distributive-law-and-how-it-works – Bumblebee Feb 22 '22 at 00:57
  • Yes, when dealing with floating point numbers on actual physical computers. – JonathanZ Feb 22 '22 at 02:24

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