What is “multiplication by juxtaposition”?

I was reading http://www.purplemath.com/modules/orderops2.htm it shows

 = 16 ÷ 2[2] + 1   (**)
 ...
 = 5 

The general consensus among math
people is that “multiplication by
juxtaposition” (that is, multiplying
by just putting things next to each
other, rather than using the “×” sign)
indicates that the juxtaposed values
must be multiplied together before
processing other operations

However when talking to certain people they all have said there is no such thing as this. There is shorthand which uses normal multiplication order and no “multiplication by juxtaposition” and etc.

Is there a “general consensus among math people” or is this simply incorrect?

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So, the question is whether $a/bc$ means $(a/b)c$ or $a/(bc)$. And the answer is, DON’T WRITE $a/bc$, because it will only cause confusion. Some people/software/whatever will make one interpretation, some will make the other, neither one has been endorsed by the Dalai Lama or any other great leader. Put in enough parentheses to make your writing foolproof.

It’s simply incorrect. If it were correct, then $2x^2$ would really mean $(2 \times x)^2 = 2^2 \times x^2 = 4 \times x^2$, but it doesn’t; it means $2 \times x^2$.

This question is more about how we deal with trolling and nuisances.

Read this page: http://knowyourmeme.com/memes/48293

Then maybe we can start a meta article about identifying and dealing with these threads.

Between the math forums that I moderate and otherwise frequent, and dozens of other forums

(a short list is here: http://www.mymathforum.com/viewtopic.php?f=13&t=20148&p=79150#p79150),

I’d guess that thousands of hours have been wasted on this garbage.

$a/bc$, which is $a/b*c$ of course means $(a/b)*c$, and that is for the same reason $a-b-c$ means $(a-b)-c$ and not $a-(b-c)$. The reason being that mathematical expressions are meant to be read from left to right when there is no operator which takes precedence.