mm-2649
===
Subject: Re: easy question about algorithm complexity
I think you didn't understand the question, which is about
algorithm efficiency. It is not even an issue whether the
algorithm produces the correct answer, but how many
operations it takes to arrive at that answer.
I assume (from what was given as the book answer)  that
only the operations in Step 2 are counted. While k<n the
operations are
compare
replace
replace
When k=n, the operations that take place are
compare
How many integers are less than n? Since we start from 0,
the answer is n. So the 3 operation loop executes n times.
How many integers equal n? Exactly one, so the 1 operation
loop executes exactly once.
So the total number of operations is 3n+1.
For n=5, the answer TO THE QUESTION ASKED is indeed 16.
Likewise for the second algorithm (where the given answer is
actually wrong, but not for the reason you think it is).
===
Subject: Re: Is a point inside a cylinder?
cylinder. This isn't the same thing as saying that if the distance is <= 
r, it *is* inside the cylinder. The point could be past the endpoints of 
the line, pass the distance test, and still be outside the cylinder. The 
locus of points a fixed distance from a line in 2D looks like a bird's 
eye view of a racetrack, not a rectangle. (A 'capsule', not a cylinder 
in 3D).
Nicholas Sherlock
===
Subject: Re: Is a point inside a cylinder?
Actually, I realize that, but part of the formula for determining the 
distance of the point to the line involved determining WHERE on the line it 

fell.  0.0 being the start point, 1.0 being the end point.  < 0.0 it was 
check for any value not falling within 0.0 and 1.0.  Which then leaves me 
the distance check. 
===
Subject: Re: It's time to ban widescreen.
hr hr.. I agree. people just don't understand widescreen means you see more. 

Just buy the right television.
filming for tv and movies are different.
-JLC
===
Subject: Re: WHAT IS THE CUBE ROOT OF INVENTORY?
Neat, took me about 10 minutes. I like this page about it the best:
http://www.borrett.id.au/computing/petals-bg.htm
Nicholas Sherlock
===
Subject: Re: WHAT IS THE CUBE ROOT OF INVENTORY?
It actually tests your ability to determine unknown rules and is more
of a test of your problem-solving skills than as a mathematician.
     --- Christopher Heckman
===
Subject: Re: another easy question
      As stated, it's an unfair question.  Evidently you're meant to 
look for a set of subsets rather than a set of elements just because the 
question uses capital X rather than lower-case x.
      The word contain is notoriously ambiguous in this context, as 
many people will say a set contains elements and also contains subsets.  
Instead of is contained in it would be better to use either the 
membership symbol or the subset symbol.  Did the book actually do that, 
by any chance?  Did you introduce the ambiguity yourself?  :-)
            Ken Pledger.
===
Subject: Re: another easy question
They also say stupid things like a subset is in the set.
===
Subject: countability, computability and continua
I was reading Roger Penrose's 'The Emperor's New Mind' recently, and an
odd thought occurred to me.
- The book had a lot of emphasis on computability, and how some numbers
are uncomputable, that is, there is no way, even in principle, of
computing the number precisely. Given any two uncomputable numbers
there is no guarantee that you'll be able to order them...
- If you remove the set of uncomputables from the reals you get the
computables. But the computables are only countable (each computable
number can be associated with a turing machine, and turing machines are
apparently also countable).
- This means that the only difference between a countable set and a
continuum is a set containing numbers for which not all pairs of
elements can be ordered!
I had a little ramble in wikipedia on the topic of ordering, and
totally ordered. But how can they be if not all members of the reals
are computable?
===
Subject: Re: countability, computability and continua
You made an unwarranted leap there.
Above you pointed out that for a given pair of uncomputable numbers 
there is no guarantee that you can order them via an algorithm.
Yet, as they are both members of the set R of real numbers, we know that 
either a <= b or b <= a. That's a basic property of R.
When you conclude that This means that the only difference between a 
countable set and a continuum is a set containing numbers for which not 
all pairs of elements can be ordered! all you're doing is repeating 
that the set of algorithmic or computerable numbers is countable.
===
Subject: Re: countability, computability and continua
Hmm... I guess so...maths is getting weirder and weirder (i'm a 2nd
year maths undergrad). So just like there's no algorithm for finding
solutions of general differential equations (something i never had an
issue with), there's no algorithm for determining the order of two
elements of R... (something which at first seemed dissatisfying) maths
seems to be full full full of things like this!
it seems to be a process of discarding every intuition and
taken-for-granted knowledge I ever had... and accepting that there is
only a small amount of knowledge we can possibly have about the
structures we invent and invented...
so are there any methods of computation asides from algorithmic
computation?
===
Subject: Re: countability, computability and continua
Part of the problem is that the 'reals' really (hoho) aren't like
anything in the 'real' world. Imho 'reals' is a really (hoho) bad name
for them, but we're pretty much stuck with it.
It's important to know that there _is_ an axiomatic basis for results,
but that doesn't mean throwing intuition out of the window completely.
It's just that we have to be aware not to _rely_ on intuition.
Have a read on the Church-Turing thesis. I'm slightly surprised it's
not mentioned in Emperor's New Mind, since it's pretty important. Have
you read Hofstadter yet?
-- 
Larry Lard
Replies to group please
===
Subject: collatz problem
I'm looking for publication about collatz problem but with 3a-1 instead  of 

3a+1. Do you know something about it.
What's the diffrent betwen 3a+1 and 3a-1 ??
Have 3a-1 period ??
MM