48÷2 (9+3) argument

What confuses most people is probably the multiplication by juxtaposition, which some consider to take precedence over normal multiplication (as does Wolfram Alpha). This is of course rubbish, but the key problem here is that people interpret these things differently, depending on convention.

For example, if I ask you to calculate 8x / 2x, you would say the answer is 4. Technically if you write it out and work left to right you will get 8 * x / 2 * x = 4 * x * x = 4x^2.

Conventionally we assume you intend to group together 8x and 2x and that you mean (8x) / (2x).
 
garp said:
Yawn. Really? Thanks for the semantics lesson. Answer is still unambiguously 288, regardless.
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Ok then, I'm glad that the non-mathematicians know better than the actual mathematicians. The world is so much better for having you guys in it.
 
To simplify it as much as possible, you could look at your personal interpretation of a/bc.

Does it mean a/(bc) or (a/b)c ?
 
Does this mean SARS made a mistake in my previous assessments? I think they owe me R 2 453 894 113.30
 
Bar0n said:
Haha, nice. I like when people throw terms like "fundamental theorem or rule" around without knowing that it actually exists.
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Yes you're completely correct. The order of precedence in calculating an equation is personal preference, a matter of taste, style, fashion even. Nothing fundamental or rule-like about it all.

We're so lucky that it's by pure coincidence that the whole world miraculously calculates equations this way so that mathematically complex things like landing a man on the moon or merely creating computer animations just randomly happen to work even though everyone makes their own deeply personal decision about what to do with these baffling lines of numbers and symbols.

Funny, though that rather a lot of sources, seem to consider this a fundamental rule of mathematics:

http://en.wikipedia.org/wiki/Order_of_operations:

In mathematics and computer programming, the order of operations (sometimes called operator precedence) is a rule used to clarify unambiguously which procedures should be performed first in a given mathematical expression.
Click to expand...
 
garp said:
Funny, though that rather a lot of sources, seem to consider this a fundamental rule of mathematics:

http://en.wikipedia.org/wiki/Order_of_operations:
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Let me quote this again:
For example, if I ask you to calculate 8x / 2x, you would say the answer is 4. (Which is something any algebra student could agree to)

Technically if you write it out and work left to right you will get:
8 * x / 2 * x
= 4 * x * x
= 4x^2.
Click to expand...

The fact is that the only people who write math so fecking poorly are 3rd graders. Yes, it's convention to work from left to right, but if you know what you're doing, you would make sure your results and formulation are both unambiguous, even taking convention into account.
 
Bar0n said:
Let me quote this again:


The fact is that the only people who write math so fecking poorly are 3rd graders. Yes, it's convention to work from left to right, but if you know what you're doing, you would make sure your results and formulation are both unambiguous, even taking convention into account.
Click to expand...

I don't hink 3rd grade math is this advanced
 
Bar0n said:
For example, if I ask you to calculate 8x / 2x, you would say the answer is 4. (Which is something any algebra student could agree to)

Technically if you write it out and work left to right you will get:
8 * x / 2 * x
= 4 * x * x
= 4x^2.
Click to expand...


Hmmm.. I don't see how you would get from 8 * x / 2 * x to 4 * x * x working from any direction. That is a completely erroneous step that is not at all suggested by the syntax or the order of precedence.
 
Definitions in mathematics are not consistent. For example:

  • Fields are usually understood to be commutative, but some authors do not assume this.
  • The set of natural numbers is usually defined as {0,1,2,...} in axiomatic set theory and subjects close to it, but as {1,2,3,...} elsewhere.
  • 0[SUP]0[/SUP] is sometimes defined to equal 1, other times it is left undefined.
 
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