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order of operations

Synonym: 
operator precedence, precedence of operations
Type of Math Object: 
Definition
Major Section: 
Reference

Mathematics Subject Classification

00A99 no label found

Comments

"Note that this isn't a problem for associative operators such as multiplication or addition in the reals. One must still proceed with caution, however, as associativity is a notion bound up with the concept of groups rather than just operators. Hence, context is extremely important."

But surely when you are talking about associativity in the context of a group, you are talking about a binary operation being associative ON a group. Hence isnt it just the same thing? You give as an example above, multiplication and addition in the reals, well the reals are a group under addition and multiplication (the fact that they are a field under both is a stronger result than they are a group under either). So the fact that we are talking about sets DOES matter - for example, you could say "the operation of multiplication is not commutative on the set of matrices".

Thats the point I was trying to get across, if I understand you correctly. I'm not sure what the contentious item of wording is. If you can figure out a better way to word things, I'll be happy to apply a correction for it.

apk

How does sigma notation affect operator precedence in an expression?

Can you be more explicit in saying what kind of cases you mean?

With a CASIO GRAPH 25+:

3.141592654 -> A
3.141592654
sin 2A
0.9939931166
sin 2*A
3.13967888

So, here, sin 2a = sin(2a) =/= (sin 2)*a = sin 2*a

Is it a nearly universal mathematical convention?

What? Convention? Of course not! idoric. At the former case the argument of sin function is{2a}, whereas in the latter one you're multiplying 'a' times sin{2}, i.e now the argument is 2 radians.

> "At the former case the argument of sin function is{2a}, whereas in the latter one you're multiplying 'a' times sin{2}, i.e now the argument is 2 radians."

This is exactly what I said but in a different way.

> "What? Convention? Of course not!"

It's not so simple, in France, not only my casio do that, but also people... but if you say it's different in another countries, ok.

Is what a universal mathematical convention? In any computer algebra system, i.e., Maple or Mathematica, if you just type in something like
sin2a or sin2*a you're going to get an error. You would need to type sin(2a) or sin(2*a). In Maple, for instance, you have to have the asterisk to denote multiplication. I guess I'm not really sure what you're asking.

I see, idoric. I don't know how Casio works out as I always have used Hewlett Packard (reverse Polish notation). But don't confuse the French people with Casio; I never saw in France such a dichotomy. It is somehow seemed like sin^{-1}x vs {sin x}^{-1}=cosec x.
perucho

> "But don't confuse the French people with Casio; I never saw in France such a dichotomy."

Before posting my question here, I questionned some (french) people: they all said "I don't know because I always put parenthesis" or "I don't remember why, but yes it's the way I always do". The casio was here just for example. It seems the origins are academical, because the teachers I questionned are all in the second category, but nobody really knows, it's a never written rule. Note that I dislike that dichotomy, so all you said is good news.

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