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Darren New wrote:
> Which just goes to show the problem I have with 90% of all matehmatical
> notation. It's so utterly inconsistent that even something like
> (f(f(x))) is ambiguous.
Several millennia of mathematical discoveries, all made by different
people in different places, and apparently several of them discovered
the same or similar things, but gave them different names - or gave them
names which clash with existing but inrelated things they didn't know about.
Just for giggles: how many meanings can you find for "normal"?
There's the normal distribution, normal vectors, a normed space...
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Invisible wrote:
> Darren New wrote:
>> Invisible wrote:
>>> What the hell is the derivative of f(f(x))?
>>
>> LMATFY
>>
>> http://www.wolframalpha.com/input/?i=derivative+of+f(f(x))
>
> FAIL.
Yes. I didn't see there were 50 responses before I posted that. :-)
> http://www.wolframalpha.com/input/?i=derivative+of+f[f[x]]
Apparently so. One of the reasons I hate mathematical notation.
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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>> FAIL.
>
> Yes. I didn't see there were 50 responses before I posted that. :-)
>
>> http://www.wolframalpha.com/input/?i=derivative+of+f[f[x]]
>
> Apparently so. One of the reasons I hate mathematical notation.
Wolfram at least have come up with a consistent, non-ambiguous notation.
In their notation, a(b)c unambiguously means the product a*b*c, and
a[b]c unambiguously means that b is the argument of function a,
multiplied by c. This is partly how Mathematica is able to determine
precisely what you meant.
Of course, nobody else uses this notation. And while *Mathematica*
rigorously follows it, *Alpha* attempts to "guess" what you mean. So in
the case above, it takes "f(f(x))" and guessees that you maybe mean "f *
f[x]", which isn't quite right. (This is what happens when computers try
to guess things...)
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Invisible wrote:
> Just for giggles: how many meanings can you find for "normal"?
Sure. But even differences between things like
sin x^-1 vs sin^-1 x
where the two "^-1" mean entirely different operations. Similarly with
lg^2 X vs lg X^2
Drove me nuts, as I learned computers before I learned all this higher-level
math.
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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>> Just for giggles: how many meanings can you find for "normal"?
>
> Sure.
Because it's not just the notations that are ambiguous - it's the
language as well!
> But even differences between things like
>
> 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?
Good luck with that one.
> Similarly with
>
> lg^2 X vs lg X^2
>
> Drove me nuts, as I learned computers before I learned all this
> higher-level math.
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...
Speaking of which, the base of natural logarithms is "e". And sometimes
"e" means 1 + 1/1 + 1/2 + 1/3 + 1/4... And sometimes "e" is just another
variable.
Hell, I've seen formulas where pi does *not* refer to the well-known
transcendental number!
Doomed, DOOMED, WE'RE ALL DOOMED! >_<
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Invisible wrote:
> But the second one? Now do you
> suppose that's the arcsine of x? Or the reciprocol of the sine of x?
That's exactly my point.
> if it does, it *probably* means the natural logarithm.
Well, that makes sense, yes.
> Doomed, DOOMED, WE'RE ALL DOOMED! >_<
I asked an exchange professor from Greece once, and he said they use the
same capital-sigma notation for summation and delta-for-change and such that
we use in America, except all their variables are also greek letters. *That*
must suck. :-)
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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Darren New wrote:
> I asked an exchange professor from Greece once, and he said they use the
> same capital-sigma notation for summation and delta-for-change and such
> that we use in America, except all their variables are also greek
> letters. *That* must suck. :-)
Heh. Mathematics, not content with featuring a zoo of custom symbols
ranging from "+" and "/" right up to those weird curly arrows, *also*
uses letters from at least the Latin, Greek and Hebrew alphabets. All at
once!
Sqrt(-1) = i [So that's Latin.]
Exp(1) = e [Latin again - except when people use Epsilon instead...]
Asin(1) = pi [Definitely Greek.]
|Z| = Alpha0 [So Hebrew then - with Arabic subscripts just for good
measure.]
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Invisible wrote:
> |Z| = Alpha0 [So Hebrew then - with Arabic subscripts just for good
> measure.]
...assuming you can SPELL. >_<
The cardinality of the set of integers is of course Aleph-null.
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Invisible <voi### [at] dev null> wrote:
> 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...
IIRC, 'log x' with no base usually means base 10, and 'ln x' is the natural log.
But, as you say, depends what the local conventions are.
> Hell, I've seen formulas where pi does *not* refer to the well-known
> transcendental number!
Now that's just careless.
> Doomed, DOOMED, WE'RE ALL DOOMED! >_<
Eat more pi.
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On Mon, 16 Nov 2009 17:12:29 +0100, Darren New <dne### [at] sanrrcom> wrote:
>
> Which just goes to show the problem I have with 90% of all matehmatical
> notation. It's so utterly inconsistent that even something like
> (f(f(x))) is ambiguous.
Although I understand (and to some extent agree with) the point you are
trying to make, (f(f(x))) is not ambiguous in mathematical notation. The
problems come when you remove parentheses or interpret them in a
non-standard manner. Wolfram Alpha does those things because mathematical
notation does not translate easily into ASCII.
--
FE
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