48÷2 (9+3) argument

Archer said:
So then it should be easy for you to point us to the rule that proves you right...
/waits forever
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There is no rule proving right or wrong. The order of operations, while commonly accepted, is not de facto. No proof exists. An equation is meaningless if it is not properly defined.

In abstract algebra for example, a well defined expression is a prerequisite before further operations can be carried out. And there are tests in place to prove that an expression is well defined.
 
Mike Hoxbig said:
There is no rule proving right or wrong. The order of operations, while commonly accepted, is not de facto. No proof exists. An equation is meaningless if it is not properly defined.
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You dont need to prove rules, the rules come before anything else. If any rules changed proofs wouldnt work anymore. BODMAS (along with the lesser known part about reading left to right) is the rule, and you follow that. Never heard anything about things outside brackets being implied as being inside.

Anyway, should we move onto how 0.999... (0.9 recururring) is equal to 1 :D
 
Mike Hoxbig said:
There is no rule proving right or wrong. The order of operations, while commonly accepted, is not de facto. No proof exists. An equation is meaningless if it is not properly defined.

In abstract algebra for example, a well defined expression is a prerequisite before further operations can be carried out. And there are tests in place to prove that an expression is well defined.
Click to expand...
There is no issue with the equation. It is well defined. a(b+c) is equivalent to a*(b+c).
 
noxibox said:
There is no issue with the equation. It is well defined. a(b+c) is equivalent to a*(b+c).
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26 pages of back and forth suggests otherwise. No serious mathematician uses ÷, it opens itself up to ambiguity. That in itself raises doubt as to the author's intention.
 
Mike Hoxbig said:
26 pages of back and forth suggests otherwise. No serious mathematician uses ÷, it opens itself up to ambiguity. That in itself raises doubt as to the readers abilities.
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Which is what we are saying (kind of)
Just read it as is, and its simple
 
Archer said:
Which is what we are saying (kind of)
Just read it as is, and its simple
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Sure, but my point is, based on what criteria? A commonly accepted guideline? The order of operations in itself is not proof that an equation needs to be solved in a certain way. It is just a commonly accepted guideline.
 
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I can't believe that there is a 25 page forum debate over a basic maths equation that should be completely obvious and unambiguous to even a high school maths student....

Any scientist, engineer, physicist, mathematician, accountant globally will calculate this as 288. If this were not the case the world would be stuffed, because if everyone made up the rules as to how to calculate an equation according to their personal philosophical preferences it simply wouldn't be possible to get anything designed, manufactured, researched, engineered, etc...
 
garp said:
Any scientist, engineer, physicist, mathematician, accountant globally will calculate this as 288. If this were not the case the world would be stuffed, because if everyone made up the rules as to how to calculate an equation according to their personal philosophical preferences it simply wouldn't be possible to get anything designed, manufactured, researched, engineered, etc...
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Scientists, engineers, physicists and mathematicians don't write expressions in a retarded manner. As for bean counters, we'll leave them out of this discussion.
 
Mike Hoxbig said:
Sure, but my point is based on what criteria? A commonly accepted rule? The order of operations in itself is not proof that an equation needs to be solved in a certain way, just a commonly accepted rule.
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Ya I dunno anymore. Its not a guideline, its a rule.
 
Archer said:
Ya I dunno anymore. Its not a guideline, its a rule.
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Rules have proof. This was just an agreed-upon guideline to help eliminate ambiguity. And even then, there are still exceptions. Hence the need for a well defined expression, and hence why nobody uses ÷.
 
Mike Hoxbig said:
Rules have proof. This was just an agreed-upon guideline to help eliminate ambiguity. And even then, there are still exceptions. Hence the need for a well defined expression, and hence why nobody uses ÷.
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Actually, no they do not.
Rules are rules
Proofs on the other hand, show the validity of a theorem (not rules). You first need rules to even begin thinking about proofs
 
Mike Hoxbig said:
Scientists, engineers, physicists and mathematicians don't write expressions in a retarded manner. As for bean counters, we'll leave them out of this discussion.
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Well, yes, but the only really objectionable part is the ÷ sign but replacing this with / has no effect whatsoever on the outcome of the equation.
 
garp said:
I can't believe that there is a 25 page forum debate over a basic maths equation that should be completely obvious and unambiguous to even a high school maths student....

Any scientist, engineer, physicist, mathematician, accountant globally will calculate this as 288. If this were not the case the world would be stuffed, because if everyone made up the rules as to how to calculate an equation according to their personal philosophical preferences it simply wouldn't be possible to get anything designed, manufactured, researched, engineered, etc...
Click to expand...

You do realize that in schools they have change the way this problem/solution is taught?
I've noticed with majority of you people <~25 they will get 2 because we were taught that 2(9+3) is considered one term very much the same as 2x and although multiplication is implied, there is no * there so if you go adding it, you are effectively breaking up the term and changing the equation.

Example
48 / 2(9+3)
let x = (9+3)
48/2x
24/x
24/(9+3)
24/12
=2

but the way older people were taught is that:
48 / 2(9+3)
let x = (9+3)
48/2x
Oh but wait 2x is actually 2 * x
So we now change the equation because you insist on adding an IMPLIED *
48/2 * x
24 * x
24 * (9+3)
24 * 12
=288

Edit: and tell me what laws if any I have broken in my first example? :rolleyes:
 
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nakedpeanut said:
You do realize that in schools they have change the way this problem/solution is taught?
I've noticed with majority of you people <~25 they will get 2 because we were taught that 2(9+3) is considered one term very much the same as 2x and although multiplication is implied, there is no * there so if you go adding it, you are effectively breaking up the term and changing the equation.

Example
48 / 2(9+3)
let x = (9+3)
48/2x
24/x
24/(9+3)
24/12
=2

but the way older people were taught is that:
48 / 2(9+3)
let x = (9+3)
48/2x
Oh but wait 2x is actually 2 * x
So we now change the equation because you insist on adding an IMPLIED * :rolleyes:
48/2 * x
24 * x
24 * (9+3)
24 * 12
=288
Click to expand...

There is NO different way to do this, it is not debatable. If kids are somehow being taught to calculate equations differently to the rest of the planet then we really are up **** creek with our educational system. It is not a matter of the "way" older or younger people are taught. It is an inviolable rule of mathematics.
 
garp said:
There is NO different way to do this, it is not debatable. If kids are somehow being taught to calculate equations differently to the rest of the planet then we really are up **** creek with our educational system. It is not a matter of the "way" older or younger people are taught. It is an inviolable rule of mathematics.
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Yet people that have tertiary educations get 2 and others 288?
 
nakedpeanut said:
You do realize that in schools they have change the way this problem/solution is taught?
I've noticed with majority of you people <~25 they will get 2 because we were taught that 2(9+3) is considered one term very much the same as 2x and although multiplication is implied, there is no * there so if you go adding it, you are effectively breaking up the term and changing the equation.
Click to expand...
Actually a term is defined as everything before or after a + or -. So 2(9+3) would only be a term if there was a + or - preceding it.

That's not my issue. My issue is that instead of being lazy, take an extra few seconds to write the damn thing over 2 lines. That will determine where the (9+3) belongs.
 
Qwikslver said:
48/2x

is not the same as
48/2*x

Two totally different equations.
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So 48/2*y is not the same as 48/2y? What operation is occurring in the case of 2y (since it isn't multiplication)? Of course if we're talking about computer code, then 2y could be a, quite probably illegal, variable name.

Mike Hoxbig said:
Sure, but my point is, based on what criteria? A commonly accepted guideline? The order of operations in itself is not proof that an equation needs to be solved in a certain way. It is just a commonly accepted guideline.
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Yes, it is proof. Those precedence rules exist for a reason. Otherwise all calculations become ambiguous.

If there is ambiguity around a(b+c) it can only be that it is multiplication or some other operation. Perhaps a() is a function that takes (b+c)?

Whether mathematicians typically use the divide symbol is neither here nor there. It was most certainly used extensively in school mathematics, and this is a school level calculation. It's exactly the kind of thing that would be used to test students to see if they know their precedence rules. There are also always going to be cases where one must use text-mode only. Trying to write an equation the way it would look in a textbook or coming out of something like LaTeX is tricky.
 
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