Spirituality
19 Mar 07
21 Mar 07
1 edit
Originally posted by adam warlockYes it is.
And saying that Z+ constitutes one half of Z' really isnt' saying much at all.
I could win a lot of money from you in any number of wagers in which I rely on the information yielded by deducing that Z+ is half of Z', with you ignoring that same information.
21 Mar 07
1 edit
Originally posted by DoctorScribblesive never read the bible, and im only in 10th grade which means i am still doing geometry which is very easy, so im not good at neither of them.
Would you say you are a better Bible scholar or a better mathematician?
edit: better at math though since i have done it before
21 Mar 07
Originally posted by DoctorScribblesI don't get it... I can't understand if you're trying to be funny or you really think that way. Anyway i don't think that it is any good giving wrong information in the forums. Saying that you can halve sets with an infinite amount of members doesn't mean anything unless you're using halving in some other sense.
Yes it is.
I could win a lot of money from you in any number of wagers in which I rely on the information yielded by deducing that Z+ is half of Z', with you ignoring that same information.
Halving set A to set B could mean that set A has twice th number of members of set B. But if set A and B have infinite members that doesn't mean nothing. And in the example you gave they had the same cardinality. So in a sense we can say that they have the same number of members.
21 Mar 07
Originally posted by adam warlockLet us make the following wager.
I don't get it... I can't understand if you're trying to be funny or you really think that way. Anyway i don't think that it is any good giving wrong information in the forums. Saying that you can halve sets with an infinite amount of members doesn't mean anything unless you're using halving in some other sense.
Halving set A to set B could mean that ...[text shortened]... e cardinality. So in a sense we can say that they have the same number of members.
An infinitely long random integer will be generated, one random digit at a time. For each digit that is even, you pay me $3. For each that is odd, I pay you $1.
What do you say?
21 Mar 07
1 edit
Originally posted by DoctorScribblesI say that I don't see your point. What that has to do with cardinality?
Let us make the following wager.
An infinitely long random integer will be generated, one random digit at a time. For each digit that is even, you pay me $3. For each that is odd, I pay you $1.
What do you say?
Edit: Or are you trying to make the point that even though the sets have the same cardinality you can make money out of it... My point in disagreeing with you was just to not see some wrong information posted on here. We can go and be all slick about it, but i think that it's more important to lay things down propperly.
21 Mar 07
4 edits
Originally posted by adam warlockHere's the proper response to my question:
see my edit.
No, I would not accept the wager because I expect to lose $2 per digit. That is because I expect half of the digits to be even and half of the digits to be odd. The terms of the wager would have to be adjusted such that I would contribute at most half of the stake per digit before I would accept it. The fact that half of the integers are even is crucial to this analysis; were I to ignore that, I could not reject the wager on the above basis. Thus, it is not only correct but can be very meaningful to partition the integers into halves.
Darvlay, ring the bell on this guy.
21 Mar 07
1 edit
Originally posted by DoctorScribbles[/b]Of course i realized that. And that's why i asked you about the money winning thing. All I'm saying is that saying that half of the integers are even isn't a very good affirmation.
Here's the proper response to my question:
of the digits to be even and half of the digits to be odd. The terms of the wager would have to be adjusted such that I would contribute at most half of the stake per digit ...[text shortened]... is not only correct but can be very meaningful to partition the integers into halves.
No, I would not accept the wager because I expect to lose $2 per digit. That is because I expect [b]half
21 Mar 07
Originally posted by DoctorScribblesI don't think there will be any bell ringing. go see some serious book on set theory and then see if they use the word half when refering to attributes of sets with infinite members. and if you do see some book like that just send me the reference of it!
Darvlay, ring the bell on this guy.
21 Mar 07
Originally posted by adam warlockMy arrogant friend, you have a long way to go on the road to attaining a level of mathematical accomplishment that entitles you to direct others' research.
I don't think there will be any bell ringing. go see some serious book on set theory and then see if they use the word half when refering to attributes of sets with infinite members. and if you do see some book like that just send me the reference of it!
21 Mar 07
2 edits
Originally posted by adam warlockA serious book on set theory will say something like "The asymptotic density of the even integers in the set of integers is one half". I still don't like Dr S's use of the verb "halve" before, though, because when we halve a number, we get a unique result, while "halving" the integers by constructing some set with density 1/2 can be done in uncountably many distinct ways.
I don't think there will be any bell ringing. go see some serious book on set theory and then see if they use the word half when refering to attributes of sets with infinite members. and if you do see some book like that just send me the reference of it!
To prove this last fact, note that there are uncountably many bounded integer sequences, because there is a bijection from the set of integer sequences in which all terms are between 0 and 9 and the real numbers between 0 and 1. Let {s(n)} be a bounded integer sequence. Then the sequence {2n + s(n)} has density 1/2 in the integers. There are thus uncountably many integer sequences of density 1/2 which differ in at least one term.
This means that to say "halve the set Z" can refer to one of uncountably many operations, while the operation "halve the number x" refers to only one thing. I don't like this recycling of words, but I agree with everything else Dr S has said in this thread.
I have decided to call people who use one word to mean two things "Al Gore linguists" in honour of Al Gore's claims of environmentalism.
EDIT Come to think of it, people who say "halve x" where x is a numer are dinosaur linguists. Thus I support Dr S's use of the verb "halve" and reject the use of "halve" in the sense of "multiply by 1/2". The real Al Gore linguist is KellyJay, who began the thread by conflating of these two different concepts on the basis that the same word sometimes gets used for both.