Notices
Results 1 to 34 of 34

Thread: Different Types of Infinity

  1. #1 Different Types of Infinity 
    Guest
    We generally call an infinitesimal number one that continues infinitely to the right side of the decimal place.

    Infinity is generally regarded as a number that continues infinitely to the left side of the number line.

    For example, .66545...., 3.13145352..., .555..., are all infinitesimals. However, it is also true that .777... is greater than .333..., therefore we should similarly suggest that 999... is greater than 777..., therefore there exists different types of infinity, some greater than others.

    However, any infinite number is greater than any finite (i.e., real), number.


    Reply With Quote  
     

  2.  
     

  3. #2 Re: Different Types of Infinity 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Ellatha
    We generally call an infinitesimal number one that continues infinitely to the right side of the decimal place.

    Infinity is generally regarded as a number that continues infinitely to the left side of the number line.

    For example, .66545...., 3.13145352..., .555..., are all infinitesimals. However, it is also true that .777... is greater than .333..., therefore we should similarly suggest that 999... is greater than 777..., therefore there exists different types of infinity, some greater than others.

    However, any infinite number is greater than any finite number (i.e., real), number.
    Except for the last sentence this is WAY out in left field.

    http://en.wikipedia.org/wiki/Non-standard_analysis

    http://en.wikipedia.org/wiki/Hyperreal_number

    http://en.wikipedia.org/wiki/Cardinal_number

    http://en.wikipedia.org/wiki/Ordinal_number


    Reply With Quote  
     

  4. #3 Re: Different Types of Infinity 
    Guest
    You, and those like you, are the reason I am not pursuing an education beyond secondary school. Leave me alone.
    Reply With Quote  
     

  5. #4 Re: Different Types of Infinity 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Ellatha
    You, and those like you, are the reason I am not pursuing an education beyond secondary school. Leave me alone.
    Then stop and think a bit before posting nonsense.
    Reply With Quote  
     

  6. #5  
    Guest
    "The so-called 'intellectuals' still look down with infinite superciliousness on anyone who has not been through the prescribed schools and allowed them to pump the necessary knowledge into him. The question of what a man can do is never asked but rather, what has he learned? 'Educated' people look upon any imbecile who is plastered with a number of academic certificates as superior to the ablest young fellow who lacks these precious documents."

    --Adolf Hitler
    Reply With Quote  
     

  7. #6  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Ellatha
    "The so-called 'intellectuals' still look down with infinite superciliousness on anyone who has not been through the prescribed schools and allowed them to pump the necessary knowledge into him. The question of what a man can do is never asked but rather, what has he learned? 'Educated' people look upon any imbecile who is plastered with a number of academic certificates as superior to the ablest young fellow who lacks these precious documents."

    --Adolf Hitler
    An accurate quote of Adolph Hitler.

    A completely inaccurate characterization of the attitude real mathematicians who are interested in ideas.

    You might more profitably spend your time on good ideas than quotes from delusional tyrants, and erroneous or inane pseudo-mathematics.
    Reply With Quote  
     

  8. #7  
    Guest
    A delusional tyrant with a genius level intellect that has convinced me of the aforementioned quote via discussion with you and other members.
    Reply With Quote  
     

  9. #8  
    Forum Ph.D. Heinsbergrelatz's Avatar
    Join Date
    Aug 2009
    Location
    Singapore
    Posts
    994
    is this something to do with Georg Cantor's set theory??
    ------------------




    "Mathematicians stand on each other's shoulders."- Carl Friedrich Gauss


    -------------------
    Reply With Quote  
     

  10. #9  
    Ots
    Ots is offline
    Forum Sophomore
    Join Date
    Jun 2009
    Posts
    103
    Quote Originally Posted by Heinsbergrelatz
    is this something to do with Georg Cantor's set theory??
    Lol!
    Reply With Quote  
     

  11. #10 Re: Different Types of Infinity 
    Moderator Moderator AlexP's Avatar
    Join Date
    Jul 2006
    Location
    NY
    Posts
    1,838
    Quote Originally Posted by Ellatha
    You, and those like you, are the reason I am not pursuing an education beyond secondary school. Leave me alone.
    Ellatha, all DrRocket did was inform you that your ideas are not correct in standard mathematics, and he knows from experience. It is clear that he knows mathematics and if you care the slightest bit about also accurately knowing and understanding mathematics, you would be wise to take what he says as the truth and use it constructively. And by not pursuing higher education you're simply letting 'those people' defeat you. If you care about mathematics at all, then learn from those who have been educated in the enormous base of knowledge that has been accumulated over hundreds (and more) of years. There is nothing wrong with that. No one is going to recreate every concept that others have come up with on their own, or improve on them without serious education in the matter, that's just the way it is.

    Please take advantage of the knowledge that you have access to and stop acting like everyone's out to get you.
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
    Reply With Quote  
     

  12. #11 Re: Different Types of Infinity 
    Guest
    Quote Originally Posted by AlexP
    Ellatha, all DrRocket did was inform you that your ideas are not correct in standard mathematics, and he knows from experience. It is clear that he knows mathematics and if you care the slightest bit about also accurately knowing and understanding mathematics, you would be wise to take what he says as the truth and use it constructively. And by not pursuing higher education you're simply letting 'those people' defeat you. If you care about mathematics at all, then learn from those who have been educated in the enormous base of knowledge that has been accumulated over hundreds (and more) of years. There is nothing wrong with that. No one is going to recreate every concept that others have come up with on their own, or improve on them without serious education in the matter, that's just the way it is.

    Please take advantage of the knowledge that you have access to and stop acting like everyone's out to get you.
    Dr. Rocket stated that he would not provide me with any aid in mathematics anymore, to which I said good. He has clearly not followed through with his statement--your statements are not convincing or impressive, and they seem to follow the routine outlined by many other members on this forum that cannot think for themselves.

    Heinsbergrelatz,
    I don't believe so.
    Reply With Quote  
     

  13. #12  
    Forum Freshman
    Join Date
    Jun 2009
    Posts
    53
    Hello Ellatha,

    I am sorry to cut in (being an inexperienced intellect myself).

    Reading from your messages, may I ask what exactly do you expect us to do then? Given that you have posted an idea of yours, what do you expect from us? To accept it and develop it further? Or to critique and improve?

    I would like to know out of curiosity.
    Reply With Quote  
     

  14. #13  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,607
    Quote Originally Posted by Heinsbergrelatz
    is this something to do with Georg Cantor's set theory??
    In fact it nothing much to do with anything, really.

    What the OPer seems to be groping toward (but failing in spectacularly) is the following: Yes there (at least) two kinds of infinity as far this term refers to the cardinality of sets.

    However, the following might be worth pointing out: if I say there are infinitely many numbers (natural, real or complex), I actually mean the sets are of infinite cardinality. This slight linguist abuse rarely confuses. However, the expression "x is an infinite (or finite) number" always does, and in fact makes little sense unless it refers to the cardinality of a set.

    Cantor showed that, whereas a set that can be put into one-to-one correspondence with a subset of the natural (i.e. counting) numbers is by definition countable (not due to him, I believe), even though it may be infinite (hence the term "countably infinite"), the set of real numbers cannot be put in such a correspondence with the set of counting numbers, and is thereby said to be "uncountably infinite".

    Unfortunately, all this seems to have been too much trouble for the OPer to check up on before posting.
    Reply With Quote  
     

  15. #14  
    Guest
    Quote Originally Posted by Guitarist
    In fact it nothing much to do with anything, really.
    You mean nothing other than mathematics. You say that my post relates to nothing, and yet you write several paragraphs discussing what it relates to. After typing up arbitrary information the subject, you bring up the dogmatic opinion that I should have "checked up" on it before posting, and yet I'm not familar with nonstandard analysis in the least. Your statements are not as insulting as you would like them to be, rather they simply make you appear like an idiot for throwing in a bunch of words that are generally taken as insulting.

    Furthermore, I'm interested in particular why you are a moderator on this forum: for an elongated period of time you posted nothing on this forum except for a promise to clear up some misconceptions in a particular thread I wrote, to which you never followed through with, and when you did finally decide to post it was because you were offended by a word that I wrote, "no."

    See my signature anid this thread (http://www.thescienceforum.com/Hospi...eem-28561t.php) for my remaining opinion.

    Tikai,
    Discuss further, bring up issues with specific points, etc...
    Reply With Quote  
     

  16. #15  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Ellatha
    ... and yet I'm not familar with nonstandard analysis in the least.
    That is painfully obvious. Non-standard analysis is the branch of mathematics in which infinitesimals are made rigorous. Your version is, not surprisingly given your self-admitted ignorance of the subject, complete nonsense.

    Unfortunately non-standard analysis has not been able to provide proofs of any theorems that cannot be proved using conventional methods.

    You would be barking up the wrong tree, if you could locate the forest.

    Rather than posting trash and expecting admiration, perhaps you ought to actually learn some real mathematics.

    If you want to understand infinite numbers, then the theory of cardinal and ordinal numbers would be a good place to start. See the links in my first post in this thread.

    On the other hand, if you still feel put upon when your errors are corrected, and consider yoursellf a mathematical genius as you have stated elsewhere in this forum, then you might consider some profesional counseling.
    Reply With Quote  
     

  17. #16  
    Guest
    Quote Originally Posted by DrRocket
    That is painfully obvious. Non-standard analysis is the branch of mathematics in which infinitesimals are made rigorous. Your version is, not surprisingly given your self-admitted ignorance of the subject, complete nonsense.
    If I did not say that this thread related to non-standard analysis, and you suggest that it doesn't, than the error lies in trying to compare the two. I did not do so; you did.

    Quote Originally Posted by DrRocket
    Rather than posting trash and expecting admiration, perhaps you ought to actually learn some real mathematics.
    When did I say I expected admiration?

    Quote Originally Posted by DrRocket
    On the other hand, if you still feel put upon when your errors are corrected, and consider yoursellf a mathematical genius as you have stated elsewhere in this forum, then you might consider some profesional counseling.
    I never said I was a mathematical genius, nor do I want any counseling. In fact, I said that I do not think like a mathematician or a scientist.
    Reply With Quote  
     

  18. #17  
    Forum Freshman
    Join Date
    Aug 2010
    Posts
    97
    I read over

    http://en.wikipedia.org/wiki/Cardinal_number

    http://en.wikipedia.org/wiki/Ordinal_number

    And I'm still not sure about something.

    My teacher said the following (in non-mathy speak):









    Is this correct? If so is it relative to:
    http://en.wikipedia.org/wiki/Cardina...er#Subtraction
    If the axiom of choice holds and given an infinite cardinal σ and a cardinal μ, there will be a cardinal κ such that μ + κ = σ if and only if μ ≤ σ. It will be unique (and equal to σ) if and only if μ < σ.
    Reply With Quote  
     

  19. #18  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by m84uily
    My teacher said the following (in non-mathy speak):









    Is this correct? If so is it relative to:
    http://en.wikipedia.org/wiki/Cardina...er#Subtraction
    If the axiom of choice holds and given an infinite cardinal σ and a cardinal μ, there will be a cardinal κ such that μ + κ = σ if and only if μ ≤ σ. It will be unique (and equal to σ) if and only if μ < σ.
    Cardinal numbers play no role in integration.

    You can say very little about the integral of a function absent any information about the function.

    So, no, what you wrote is not "correct".
    Reply With Quote  
     

  20. #19  
    Forum Ph.D. Heinsbergrelatz's Avatar
    Join Date
    Aug 2009
    Location
    Singapore
    Posts
    994
    Quote Originally Posted by Guitarist
    Quote Originally Posted by Heinsbergrelatz
    is this something to do with Georg Cantor's set theory??
    In fact it nothing much to do with anything, really.

    What the OPer seems to be groping toward (but failing in spectacularly) is the following: Yes there (at least) two kinds of infinity as far this term refers to the cardinality of sets.

    However, the following might be worth pointing out: if I say there are infinitely many numbers (natural, real or complex), I actually mean the sets are of infinite cardinality. This slight linguist abuse rarely confuses. However, the expression "x is an infinite (or finite) number" always does, and in fact makes little sense unless it refers to the cardinality of a set.

    Cantor showed that, whereas a set that can be put into one-to-one correspondence with a subset of the natural (i.e. counting) numbers is by definition countable (not due to him, I believe), even though it may be infinite (hence the term "countably infinite"), the set of real numbers cannot be put in such a correspondence with the set of counting numbers, and is thereby said to be "uncountably infinite".

    Unfortunately, all this seems to have been too much trouble for the OPer to check up on before posting.
    Thanks for that brief description regarding set theory. Though most of the terms like cardinal numbers and ordinal numbers are pretty new to me. I just got to know about them 2 weeks ago when i was reading about Georg Cantor's work in the book "God created the integers"- stephen hawking, and so far im not doing a great job understanding the whole thing . Nevertheless i find it very interesting indeed.
    Just a question, when i was reading about Cantor's work, this number called Aleph number came out. How do you write the "Aleph" the hebrew letter in terms of TeX???
    ------------------




    "Mathematicians stand on each other's shoulders."- Carl Friedrich Gauss


    -------------------
    Reply With Quote  
     

  21. #20  
    Forum Freshman
    Join Date
    Aug 2010
    Posts
    97
    Quote Originally Posted by DrRocket
    Quote Originally Posted by m84uily
    My teacher said the following (in non-mathy speak):









    Is this correct? If so is it relative to:
    http://en.wikipedia.org/wiki/Cardina...er#Subtraction
    If the axiom of choice holds and given an infinite cardinal σ and a cardinal μ, there will be a cardinal κ such that μ + κ = σ if and only if μ ≤ σ. It will be unique (and equal to σ) if and only if μ < σ.
    Cardinal numbers play no role in integration.

    You can say very little about the integral of a function absent any information about the function.

    So, no, what you wrote is not "correct".
    What if I were to clarify and say:

    Reply With Quote  
     

  22. #21  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Heinsbergrelatz
    Thanks for that brief description regarding set theory. Though most of the terms like cardinal numbers and ordinal numbers are pretty new to me. I just got to know about them 2 weeks ago when i was reading about Georg Cantor's work in the book "God created the integers"- stephen hawking, and so far im not doing a great job understanding the whole thing . Nevertheless i find it very interesting indeed.
    Just a question, when i was reading about Cantor's work, this number called Aleph number came out. How do you write the "Aleph" the hebrew letter in terms of TeX???


    To learn about cardinals and ordinals a good source is Naive Set Theory by Paul Halmos.
    Reply With Quote  
     

  23. #22  
    Forum Ph.D. Heinsbergrelatz's Avatar
    Join Date
    Aug 2009
    Location
    Singapore
    Posts
    994
    Quote Originally Posted by DrRocket

    To learn about cardinals and ordinals a good source is Naive Set Theory by Paul Halmos.
    Thanks for the source. Oo and how did you write that using TeX??
    For the undergraduate mathematics courses, is set theory usually taught if you are going for mathematics as a major??
    ------------------




    "Mathematicians stand on each other's shoulders."- Carl Friedrich Gauss


    -------------------
    Reply With Quote  
     

  24. #23  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Heinsbergrelatz
    Quote Originally Posted by DrRocket

    To learn about cardinals and ordinals a good source is Naive Set Theory by Paul Halmos.
    Thanks for the source. Oo and how did you write that using TeX??
    For the undergraduate mathematics courses, is set theory usually taught if you are going for mathematics as a major??

    You shoild see the code in the window when you reply.



    \aleph
    Reply With Quote  
     

  25. #24  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,607
    Quote Originally Posted by Ellatha
    Furthermore, I'm interested in particular why you {i.e. me}are a moderator on this forum:
    It is considered Very Bad Form on this forum to openly challenge a moderator's credentials, though not strictly "illegal".

    If you (or any one else for that matter) truly believe I am not "up to the job" then please, by all means, complain to the admins, currently In(Sanity) and SkinWalker.

    Though I was very active, possibly over-active in the past, the reason for my recent lack of posting here is well known to my favourite members. Does that disqualify me from deleting viagra, shoe and iPhone adverts? Believe me, that is most of what I do here
    Reply With Quote  
     

  26. #25  
    Guest
    I just find it annoying that you would think that using your posting time to attack my character is more important than increasing discussion on mathematical matters. I do not care about this (or any other) forum enough to complain.
    Reply With Quote  
     

  27. #26  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Ellatha
    I just find it annoying that you would think that using your posting time to attack my character is more important than increasing discussion on mathematical matters. I do not care about this (or any other) forum enough to complain.
    Guitarist did not, ever, attack your character. He is far to circumspect, and even-handed to do that. Guitarist suffers fools gladly.

    I do not, in public forums where they pose a threat to the naive but genuinely curious.

    You have made the transition from the genuinely curious to someone posing as knowledgeable but posting only the false or trivial. You are doing an excellent job of making a fool of yourself via the objective content, or lack thereof, in your posts. Guitarist's comments were very clearly directed toward that content, and therefore toward "increasing discussion of mathematical matters".
    Reply With Quote  
     

  28. #27  
    Guest
    Quote Originally Posted by DrRocket
    Guitarist did not, ever, attack your character.
    Interesting than that he admitted to insulting me. Stop scanning, and start reading.

    I'm interested in the results of the following experiment, for the sake of my argument:

    Measure your heart rate at its normal level. Read the following statement:

    "I am several times smarter than Isaac Newton."

    Measure the heart rate at its apex, and subtract what it was at its normal level.

    I think the results will demonstrate that your emotions blind your intellect to a tremendous extent; you would do yourself well to fix this problem.
    Reply With Quote  
     

  29. #28  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Ellatha
    Quote Originally Posted by DrRocket
    Guitarist did not, ever, attack your character.
    Interesting than that he admitted to insulting me. Stop scanning, and start reading.
    Guitarist has made precisely two posts thus far in this thread :

    Quote Originally Posted by Guitarist
    In fact it nothing much to do with anything, really.

    What the OPer seems to be groping toward (but failing in spectacularly) is the following: Yes there (at least) two kinds of infinity as far this term refers to the cardinality of sets.

    However, the following might be worth pointing out: if I say there are infinitely many numbers (natural, real or complex), I actually mean the sets are of infinite cardinality. This slight linguist abuse rarely confuses. However, the expression "x is an infinite (or finite) number" always does, and in fact makes little sense unless it refers to the cardinality of a set.

    Cantor showed that, whereas a set that can be put into one-to-one correspondence with a subset of the natural (i.e. counting) numbers is by definition countable (not due to him, I believe), even though it may be infinite (hence the term "countably infinite"), the set of real numbers cannot be put in such a correspondence with the set of counting numbers, and is thereby said to be "uncountably infinite".

    Unfortunately, all this seems to have been too much trouble for the OPer to check up on before posting.
    Quote Originally Posted by Guitarist
    It is considered Very Bad Form on this forum to openly challenge a moderator's credentials, though not strictly "illegal".

    If you (or any one else for that matter) truly believe I am not "up to the job" then please, by all means, complain to the admins, currently In(Sanity) and SkinWalker.

    Though I was very active, possibly over-active in the past, the reason for my recent lack of posting here is well known to my favourite members. Does that disqualify me from deleting viagra, shoe and iPhone adverts? Believe me, that is most of what I do here
    As anyone can clearly see the content of your posts, not your character, is the subject addressed by Guitarist. Now, you may personally take criticism of the content of your post as an insult or an attack on your character, but an objective reader would not.

    If there was any insulting I would opine that it was in your reply to Guitarist, though a "rapier-like wit" seems to be absent:

    Quote Originally Posted by Ellatha
    You mean nothing other than mathematics. You say that my post relates to nothing, and yet you write several paragraphs discussing what it relates to. After typing up arbitrary information the subject, you bring up the dogmatic opinion that I should have "checked up" on it before posting, and yet I'm not familar with nonstandard analysis in the least. Your statements are not as insulting as you would like them to be, rather they simply make you appear like an idiot for throwing in a bunch of words that are generally taken as insulting.

    Furthermore, I'm interested in particular why you are a moderator on this forum: for an elongated period of time you posted nothing on this forum except for a promise to clear up some misconceptions in a particular thread I wrote, to which you never followed through with, and when you did finally decide to post it was because you were offended by a word that I wrote, "no."

    See my signature anid this thread (http://www.thescienceforum.com/Hospi...eem-28561t.php) for my remaining opinion.
    Reply With Quote  
     

  30. #29  
    Guest
    Do you ever know what's going on? The points I made related to content outside of this thread; your continually demonstrate a clear lack of understanding of what's being discussed.
    Reply With Quote  
     

  31. #30  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Ellatha
    Do you ever know what's going on? The points I made related to content outside of this thread; your continually demonstrate a clear lack of understanding of what's being discussed.
    So, one is supposed to understand that your post, in this thread, has nothing to do with the content of this thread.

    You tell me that you have some enormous IQ. Then why do you say such incredibly stupid things ?

    BTW, my characterization of the gentlemanly deportment of Guitarist and his willingness to suffer fools gladly extends well beyound the bounds of this thread. So, despite your widening of the basis for your criticism of Guitarist, you are still WAY off base.

    Put a sock in it.
    Reply With Quote  
     

  32. #31  
    Guest
    Quote Originally Posted by DrRocket
    So, one is supposed to understand that your post, in this thread, has nothing to do with the content of this thread.
    If you do not understand what is being discussed, than stop pretending that you do: you are only doing the public a disservice in pretending that you do.

    Quote Originally Posted by DrRocket
    You tell me that you have some enormous IQ. Then why do you say such incredibly stupid things ?
    I refrained from doing so in the public forum in order to not appear arrogant to the public while still addressing a previous point. You have childishly chosen to simply reveal the content that I attempted to conceal. Grow up.

    Quote Originally Posted by DrRocket
    BTW, my characterization of the gentlemanly deportment of Guitarist and his willingness to suffer fools gladly extends well beyound the bounds of this thread. So, despite your widening of the basis for your criticism of Guitarist, you are still WAY off base.

    Put a sock in it.
    God forbid anyone offend your precious ego; maybe I should have gone so far as to lie in order to make you happy. Needless to say the word childish exemplifies your behavior.
    Reply With Quote  
     

  33. #32  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,607
    Quote Originally Posted by DrRocket
    To learn about cardinals and ordinals a good source is Naive Set Theory by Paul Halmos.
    I fully endorse this recommendation. I found it as a used hard cover the back end of last year for fractionally over 10 euros on Amazon (or was it Alibris?). It is a really nice tour around what it says on the cover.

    Of course, set theory in all its glory, is more than Halmos offers (by his own admission) and is, speaking for myself, a rather dry - not to say arid - subject. But each to their own.

    Whether or not set theory in any form is a mandatory course in undergrad math courses, I am not (of course) qualified to say. I will simply throw out this.....

    ,,,,,in so-called "advanced" mathematics you will have to go quite a distance to find a mathematical object (ring, field, group, vector space,....) that cannot be said to be a SET with some additional algebraic structure. If this is true (I think it is, though I can think of at least one exception), then an understanding of naive set theory is, at the very least, helpful.

    The exception I am thinking of are topological spaces, which, just being sort of "jazzed up" sets, require an even deeper understanding of set theory, though I cannot convince myself they are algebraic in the loose sense that I used above. Likewise, manifolds are sort of "jazzed up" top. spaces, so the same applies.

    PS I apologize for my imprecise language here, I hope it was not too confusing
    Reply With Quote  
     

  34. #33  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Guitarist
    Quote Originally Posted by DrRocket
    To learn about cardinals and ordinals a good source is Naive Set Theory by Paul Halmos.
    Of course, set theory in all its glory, is more than Halmos offers (by his own admission) and is, speaking for myself, a rather dry - not to say arid - subject. But each to their own.
    There are three very appealing characteristics of Halmos's book

    1. As you note, it is inexpensive.

    2. It is not nearly as dry and arid as axiomatic set theory (a sure cure for insomnia)

    3. It is quite short (see item 2).
    Reply With Quote  
     

  35. #34  
    Forum Freshman
    Join Date
    Nov 2011
    Location
    Sweden
    Posts
    39
    Quote Originally Posted by Heinsbergrelatz View Post
    is this something to do with Georg Cantor's set theory??
    Yes, Georg Cantor created a whole hierarchy of transfinite (i.e. beyond finite) numbers. The great mathematician David Hilbert called this vast domain, rich for
    mathematicians to study, 'Cantor's paradise'.
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •