Quote:
Originally Posted by Bill Verburg
unfortunately that is not true
the basic properties are the foundation of all mathematics, it's when people make up rules that confusion and inconsistent results pop up
I suggest that you go rear a basic math text
the associative property is the only one that allows the addition of a parentheses that was not explicitly written in the problem
it is usually given as abc =(ab)c =a(bc) or a+b+c = (a+b)+c = a+(b+c)
it allows the introduction of a parenthesis so as to alter the order of operations, it is not allowed when division and subtraction are involved. This is the only way a parentheses can be added to an expression.
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Bill, Bill, Bill......
Mathematical convention - AoPSWiki
Math 1010 on-line
A "convention" is not mathematics. It's not a basic property of mathematics. Solving from left to right is a convention. Tomorrow, the notation could be changed to right to left and the mathematics would still work. We use infix notation today. That is a convention. Sometime in the future, it could be decided that we will be using postfix (Reverse Polish) notation. The mathematics would still be the same.
If the mathematics community decided that implicit multiplication (juxtaposition) has precedence over division or explicit multiplication, only the notation would change. The mathematics would be unaffected.
Don't go confusing conventions with properties of mathematics or the foundations of mathematics.
Scott