Re: parentheses


sizors_1@xxxxxxxxxxx wrote:
Is it correct to say that *all* mathematical expressions should
properly be enclosed within parentheses, even though often parentheses
are omitted?

I wouldn't say it's necessarily correct, but it could be used in some
contexts.

Even a seemingly simple example like 12 x 4 suggests that
12 has parentheses, otherwise 12 x 4 = 10 + 2 x 4 = 18, and obviously
12 x 4 is never interpreted this way. So isn't it technically correct
to write (12) x 4?

In this case, I would say no. You are confusing the number with its
representation. It's only 10+2 because you chose to use Base 10.
Had you used Base 16, the representation is C. How can a number
be both an expression and not an expression simultaneously?

Or perhaps you should go all the way and write
((12) x (4)). The outermost parentheses could be important in cases of
substitution, but I see no reason to enclose the single digit 4 in
parentheses.

You would if you wrote computer programs.

Nonetheless what I'm interested in is the proper syntax
(formation) rules for expressions. I've seen inconsistencies in
different texts. For example, in Gries' A Logical Approach to Discrete
Math, he *first* says that constants like 231 are expressions, and
*then* says that if E is an expression, then (E) is an expression.

I don't see that as an inconsistency.

In MS-Access, a calculated field gets a default name indicating
it is an expression

Expr1: [Result]*4

and it's still an expression regardless of whether or not there are
multiple terms/operators

Expr2: [Result]
Expr3: 4

Isn't this incorrect based on the example I cite above?

The fact that "12" is an expression doesn't mean that it's "10+2".

Another
example would be negative intergers like -12? Shouldn't this be
expressed (-(12)), otherwise -12 = -10 + 2 =
-8.

No, because 4 is also an expression even though you can't break
it apart like you can 12.

My bottom line question is, are *all* mathematical expressions --
including variables like x, y, etc., properly defined as being enclosed
in parentheses, even in cases where parentheses wouldn't seem
necessary?

My opinion is still no.


Thanks

.

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