so glad to see you are keeping the banner of clear thinking flying. As a
former professor of computer science and also a past member of the ANSI
committee that standardized C (the computer language), I very much
believe in the educational value of testing one's theories on a
computer. Helps to keep a person intellectually honest.
So I appreciate your suggestion to these posters to try their examples
in Mathematica. For those who do not have access to this very
sophisticated program, most of the current computer languages will
suffice to make the underlying principles of precedence and
associativity clear. C, C++, Java, Python, etc. all use the same
standard evaluation order for arithmetic expressions. There is one
caveat, though: none of these languages use square brackets for
grouping, and none allow simple juxtaposition as a shortcut for
multiplication.
So,
16 / 2 [8 – 3 (4 – 2)] + 1
would have to be rewritten as
16 / 2 * (8 – 3 * (4 – 2)) + 1
Here are two websites that may help:
http://www.algebra.com/algebra/college/abstract/Associativity.wikipedia
http://msdn2.microsoft.com/en-us/library/ms139741.aspx
Please note that in mathematics terminology, a left-associative operation is a non-associative operation that is conventionally evaluated from left to right. This refers to one operator only, as in 16/2/2.
In computer science, left-to-right associativity is also defined for an admixture of two or more operators of the same precedence level, as in 16/2*2.
Best regards,
Michael
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