Occam's razor referrs to solutions or explanations not definitions. From wiki; "To straightforwardly summarize the principle as it is most commonly understood, “Of several acceptable explanations for a phenomenon, the simplest is preferable.”

Often restated "the simplest solution or explanation tends to be the right one"
which, absent the equivicating term "tends", I agree is demonstrably false.

But relevant to this topic more properly stated "entities should not be multiplied unnecessarily" applies to the wiki "Primality of one" point regarding 1x1x1x3=1^3x3=3 in that it multiplies entities unnecessarily. So the preferred definition of 3 is 3=1x3=1(3) not 1x1x1x3=1^3x3=3. Although 1x1x1x3=1^3x3=3 is true it is not preferred. Multiplication (the reverse of division) is defined in terms of addition not in terms of multiplication of multiplication.


I agree that "whole" numbers could and should be logicly added to the simple definition to avoid the quandry you defined. However, absent an equivicating statement, it is usually assumed (as a mathematical convienience) that the numbers are whole when the product is required to be whole. Just as 1 times n is assumed and not written (as a mathematical convienience) for any number or expression as in 1=1x1=1(1) or 2 =1x2=1(2) or a =1xa=1(a)=1a.

PS I am obliged to point out that this discussion is getting into areas of math that could require written mathematical statements which could be written in html coding but unsupported by the BAUT forum software for some reason. For this reason I am going to have to tell you that should an answer requiring unsupported code be needed I am going to state the permitted response "I DON"T KNOW" how to answer without html coding". Also if an answer requires a criticism of the questioner's mathematical or scientific principle or premise I am going to answer "I DON'T KNOW how to answer your question without criticising your principles or premis and being fouled by a moderator here". I write this because there are statements above that do not belong in this discussion.