Re: Calculus Query
 

Manoel, you are brilliant. I just went through this with a teammate, and while your explanation was a bit hard to follow (not your fault, ours) we eventually got it (and checked it with my brick of a TI-92). Highest compliments man! How old are you? (EDIT: Ah, I didn't see you were a mentor, I thought you were a student) This demonstrates rather impressive intuition.

An alumni emailed me a 4 page proof that there wasn't such a function, thanks for putting him in his place. :D

What regional are you attending this year?

Re: Calculus Query
 

Leo M and phrontist,

Thanks for the compliments! As I told you, it was a joint effort - a buddy helped me with that one.
At first I thought (like everyone) that there wasn't such a function, and spent some time trying to prove that. Since I'm studying to become an Engineer, and not a Mathematician, that formal, axiom driven kind of math doesn't go well with me, so I gave up.
Better than proving that it didn't exist would be finding such a function, so that's what I tried to do next.
I looked at the common forms of functions - exponential, trigonometric, etc. - and did a quick check. That quick check threw me off, because I was considering only integer exponents and that didn't cut it.
I had to try functions of the form e^x, because that's the answer to pretty much everything ;), and then came the idea to try an exponent that when inverted would be itself minus one. If I had remembered the golden ratio in the first place, I'd have arrived at the answer quicker. :D

Phrontist,
I agree my explanation wasn't very easy to follow; I should have explained some passages a little better, but I was trying to do a one-pager. :p
Add to that the fact that I lack the proper technical English knowledge and you got what you got. :ahh:
The only thing I hate more than a bad explained deduction is one that is "left as an exercise to the student". :rolleyes:
I'm a mentor but a young one, I'm just 20 and on my way to receiving a BSEE, somewhere around 2007 (Engineering takes five years in Brazil).
We'll probably be going to Boston this year, if you make it to the MIT (and I sure hope you do!) make sure to stop by!
Care to share that 4-page proof? I'd like to take a look at it, if possible.

Yeah, I just threw the graphic to show its reflection around the y=x line. Computer graphs are bad, but one that goes from -infinity to infinity is even worse!
By the way, I'm a big fan of yours for that sine/cosine approximation you shared with us back in the PBasic days. Good stuff, man, good stuff!

Re: Calculus Query
 

Somewhere, Leonardo da Vinci is smiling:

http://www.mcs.surrey.ac.uk/Personal.../fibInArt.html

And a mathematician's perspective -

http://mathworld.wolfram.com/GoldenRatio.html

My brain hurts after reading through that.


I enjoyed reading through your solution as well. Good job!

Re: Calculus Query
 

Like the Fibonacci series itself, it just goes on and on :

http://www.mscs.dal.ca/Fibonacci/

Fibonacci Association, Fibonacci Quarterly..................

I have been a plant engineer for fifteen years +, and sometimes I
really need something more than pipe leaks, burned-out motors,
and managers running around 90 miles an hour with their hair on fire.

It regenerates something deep inside me to work on the clever problems and talk to the ingenious people.

Here's a question I've been wondering about.

Who do you think will be the first First person to win a Nobel Prize?

Maybe that's poorly phrased and a separate thread besides, but I wonder sometimes whether I am communicating with a future prize winner. I hope I live long enough to see it (I am a year older than Dean).

I'd sure love to see one of you guys in Stockholm, with dean and Woodie in the audience.

Re: Calculus Query
 

Bad news! My teammate has carefully explained to me that we have all been deceiving ourselves :(

Quoth the amazing Dustin:

Re: Calculus Query
 

Maybe I am extraordinarily dense this morning, but I cannot follow this argument at all.

"f^-1(f(z))=f(f^-1(z))=z
z=-1.0"

The first equation is just a way of defining the inverse of a function. The second (z=-1) is just a statement assigning a value to z, and does not follow from the previous statement at all. In the words of Wolfgang Pauli, "That isn't right. That isn't even wrong."

"inv f(x) is a function of y, not x, it would have to be expressed as + and – 1.202x^0.618 for graphing on your calculator (on the interval of 0 to infinity)(considering the x axis to be the domain, which in reality it is not), which is not the same as the derivative operation on f. Look at the graph!!!!!!!! If you would of said of such a constraint, that the function didn’t have to be on its full sets which is in R^2 for the domain and range of said function, then yes this is true, but that’s not the real definition of a function!"

If anyone can explain what the above statements mean, I'd be happy to listen, but as they stand they do not appear to be anything but randomly arranged pseudo-mathematical jargon with lots of !!! thrown in.


"You wonted a proof and that’s what I gave you, you have to be very specific on your definitions when considering such a problem, next time be true to the language or include exceptions or I wont bother with such problems. "

Concerning the above statement, in legal terms: re ipso loquitor - the thing speaks for itself.

Manoel is still correct.

Re: Calculus Query
 

As Leo M, I'm not sure I got it right.

Anyway, here are two possible readings:
- The aforementioned function is not a function because a function's domain and range has got to be (-infinity, infinity). Well, that's certainly not the definition of a function (neither a requirement) and many "well established" functions do not fulfill those requirements. Ex: y=sqrt(x), y = tan x, ...
- The function is no good because it is not defined for "z"=-1 (not sure why that came up). Again, that's wrong, because the function's domain is [0, infinity) and we're all OK with it.

As those possibilities were easily refuted, I'm pretty sure I just didn't understand what Dustin was trying to say. Maybe some punctuation (and please, don't take it the wrong way) or the 4-page proof could help us here.

Regards,