Math Is Fun Forum

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Power Set Algorithm

Pi is, by definition, the ratio of the circumference of a circle to its diameter.  Are you arguing that such a ratio cannot exist?

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Wrap it in bacon

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Power Set Algorithm

It looks like George,Y is trying to express technical ideas by using non-technical terms and/or using the wrong technical terms for what he has in mind. This is the source of all the misunderstanding from Asad Paki’s completely unnecessary bumping of the thread onwards. I hate this when this happens.

Okay, I’ll try and paraphrase a snippet of George’s drivel in more comprehensible mathematical terminology so everyone can make some sense of it.

3, 3.14, 3.141, 3.1415, ...
is what we did find and what we can continue improving

{3, 3.14, 3.141, 3.1415, ...} (the whole of the series)
is exaggeration, which is not proved.

Paraphrase:

Consider the sequence {3, 3.14, 3.141, 3.1415 …} up to some millionth or billionth decimal place. This is a finite set of numbers, and any practical calculation of π is limited by the last number of the set. We can however improve on the precision of our practical value of π.

The whole of the sequence {3, 3.14, 3.141, 3.1415 …} is an infinite extension of our finite set above, including missing numbers we have yet to calculate. It is not possible to calculate all the numbers in this infinite sequence though.

There. The other parts of George’s nonsense can be similarly paraphrased.

Last edited by JaneFairfax (2009-02-04 11:37:05)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Power Set Algorithm

George, I'm all for discussing this further.  However, I have stated many times that you should start a topic specifically on the real numbers, properties of infinity, etc.  You refuse to do so, and I can't imagine a reason why.  This is a thread about an algorithm to generate a power set, and you have now turned it into a thread on rational/irrational/countable/infinity/indefinite.

Since this is an old thread, I will allow it to continue here (i.e. feel free about continuing to post on this topic),  but if you start polluting other threads I will begin moderating more heavily.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Power Set Algorithm

I started a thread for you, George

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Power Set Algorithm

Thank you Ricky. This is mainly because I haven't group all the ideas into a system. Now I just have inspirations on this on that and I am still reading new chapters. I happened to read Cohen's proof on Cantor's Continuous Assumption, which is the amount(cardinality) of all real numbers is 2 to the exponential of the amount of natural numbers. And he did used forcing, the binary digits. And from there I start speculation that although it is long, it is possible to order the 2[sup]N[/sup] of all real numbers between 0 and 1.

Thank you JaneFairFax for your clarification and wording. Although I don't agree with your opinion.

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X'(y-Xβ)=0

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Power Set Algorithm

Are you arguing that such a ratio cannot exist?
Yes I do dude. Seeing is not believing. Please read my post in "This is cool" and you will find my argument that the existence of a circle in not testified or verified by science discoveries so far. And read my recent disproof that infinite decimals has its consistency problem.

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X'(y-Xβ)=0

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Power Set Algorithm

Are you arguing that such a ratio cannot exist?
Yes I do dude. Seeing is not believing. Please read my post in "This is cool" and you will find my argument that the existence of a circle in not testified or verified by science discoveries so far. And read my recent disproof that infinite decimals has its consistency problem.

I think you're misunderstanding what mathematics is. Science has absolutely no relevance to maths; the concepts we deal with in maths are all hyopthetical. Of course a perfect circle could not exist in our universe, but it does exist in the hypothetical, mathematical universe that we have created, and therefore so does pi.

Last edited by Daniel123 (2009-02-07 08:44:41)

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Power Set Algorithm

Well how about pi itself unresolvable logic inconsistency? Do you still accept it? Or at least will you state it is proven?

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X'(y-Xβ)=0

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Power Set Algorithm

1 It is not empirical, that means no evidence in our real world consolidates its existence
2 It is paradoxical. This denies its soundness in the world of concepts. If you accept two numbers, each is larger than another, I have nothing to say. But if not, please note the inconsistency of the concept of infinite decimals.

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X'(y-Xβ)=0

vikash.madhow

Member

Registered: 2009-04-05

Posts: 1

Re: Power Set Algorithm

The following Java code will generate all distinct sublists of a specified size from a list. This is equivalent to the generation of all subsets of a specified cardinality from the supplied set (List abstraction is used instead of Set for convenience of the API to this recursive method) . By calling this method for size 0 to N where N is the cardinality of the set, you will get all elements of the powerset.

    
    /** Returns all combinations of items of the specified size from the source
     *  list. Order is preserved, such as if a is always before b in the source,
     *  there will not be a combination where a is after b. Unlike permutations,
     *  order is not significant such that [a,b] is equivalent to the combination
     *  [b,a] and therefore latter will not be returned unless a or b appears
     *  more than once in the source list. */
    public static <T> List<List<T>> getCombinations(List<T> source, int size) {
        if (size < 0 || size > source.size())
            throw new IllegalArgumentException("Combination size must be greater " +
                "than or equal to 0 and less than or equal to the size of the " +
                "source list (" + source.size() + "). Current size of " + size +
                " is invalid.");

        List<List<T>> combinations = new ArrayList<List<T>>();
        if (size == 0)
            combinations.add(new ArrayList<T>());
            
        else if (size == source.size())
            combinations.add(new ArrayList<T>(source));

        else
            for (int i = 0; i < source.size() - size + 1; i++) {
                T head = source.get(i);
                List<T> subList = source.subList(i + 1, source.size());
                for (List<T> subCombination: getCombinations(subList, size - 1)) {
                    subCombination.add(0, head);
                    combinations.add(subCombination);
                }
            }
        
        return combinations;
    }

V.