Neeum Zawan wrote:
> On 11/16/09 10:33, Invisible wrote:
>>> sin x^-1 vs sin^-1 x
>>>
>>> where the two "^-1" mean entirely different operations.
>>
>> The first one, at least, is unambiguous. But the second one? Now do you
>> suppose that's the arcsine of x? Or the reciprocol of the sine of x?
> 
>     I think you'd be hard pressed to find someone who has used it to
> mean the reciprocal of the sine. Perhaps that's why they defined the
> cosecant?
> 

Neither is unambiguous, really. The first one I might read as either
(sin x)^-1 or sin(x^-1). The second I have seen used to represent both
cosecant and arcsin. All depending on which professor was scribbling the
function.

>> And then of course, people will write "log x". Wanna take a guess which
>> base that is? Now, sometimes it actually doesn't matter which base. And
>> if it does, it *probably* means the natural logarithm. Probably...
> 
>     Go back far enough, and it always meant base e. I wonder when ln(x)
> notation cropped up.
> 
>     If it doesn't matter what base it is, then it'd be "obvious" from
> the context.
> 

My high school and college professors learned from a different book.
ln(x) was always natural log, while log(x) was either base 10 for the
normal math courses or base 2 for the computer courses. Most of the
time, people were expected to place a subscript noting the base.

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