• Infinites outside of math?
    f is onto Y if and only if (f is a function & range(f)= Y)TonesInDeepFreeze

    Indeed. So N can't be mapped 1-1 onto. You can at most map N to infinite points, infinite times. Say 1 into 2, 2 into 4, 3 into 6, etc. But into still. Then you still need to map into all inbetween intervals. On each interval an infinity of infinities of naturals is needed. So you need inf^3 times to map N into R. Pffffff.... I'm done! Thanks for the resistence! :smile:
  • Infinites outside of math?


    I can map N onto R infinite times infinite times.

    Infinite times onto

    [0.1-0.99999...]
    [0.01-0.09999...]
    [0.001-0.009999...]
    .
    .
    .
    So infinite times onto [0-1]. The map even defines [0-1].

    Times infinity for all length 1 intervals.

    So in total there is an inf^3 involved. Hence aleph1.4. Merry Christmas!

    No. You are right. Onto only for N^3! But into inf^3 times. I get sleepy.

    Which means aleph1.4 is the one for R, and aleph2.6 is the one for RxR.
  • Infinites outside of math?
    So? Not everything on the Internet is the sharpest formulationTonesInDeepFreeze

    There you go.
  • Infinites outside of math?
    R is onto Y if and only if (R is a relation & Az(zeY -> Ej <j z> e R))TonesInDeepFreeze

    Huh?
  • Infinites outside of math?
    Anyway, now you can see why there is no function f with a singleton domain an d onto R.TonesInDeepFreeze

    Still, I can map N onto R. Inf^3 times even...
  • Infinites outside of math?
    That's not quite right or at best awkward,TonesInDeepFreeze

    I got it from the net...
  • Infinites outside of math?
    You guys need to get a hotel room.TonesInDeepFreeze

    Haha! In Hilbert's hotel! Wrong post...
  • Infinites outside of math?
    Are you off your meds again?jgill

    I now even think R has cardinality aleph1.4!

    You guys need to get a hotel room. — jgill

    Haha! In Hilbert's hotel!
  • Infinites outside of math?


    "The mapping of 'f' is said to be onto if every element of Y is the f-image of at least one element of X."

    Y=R, N=X...
  • Infinites outside of math?
    So which is it now? You claim that card(R) = aleph_1, thus asserting the continuum hypothesis? Or you deny that card(R) = aleph_1, thus denying the continuum hypothesisTonesInDeepFreeze

    No. I assert card(R)=aleph1.4. Call me crazy, like you wish. Card(RxR)=aleph2.6, more or less. 2^(1.4)=3, more or less, 2^(2.6)=6, more or less.

    Then either you are insane or you don't know the meaning of 'map onto'.TonesInDeepFreeze

    I can send every cardinal on top of R. On top where I send it into.
  • Infinites outside of math?
    I think we have discovered a real infinity in life, which is what this post is about. You and me commenting on each other. I may be in flat contradiction with what I thought previously, that's right. But not with my present self. But for sure with you....
  • Infinites outside of math?
    So you are in flat out contradiction with yourself.TonesInDeepFreeze

    So?
  • Infinites outside of math?
    Of course one can map a singleton set INTO R.

    But there is no map of N ONTO R
    TonesInDeepFreeze

    I can map a singleton on R too. No problem.
  • Infinites outside of math?
    Yet you say you disagree with the continuum hypothesis now, while you have been claiming it in dozens and dozens of postsTonesInDeepFreeze

    So?
  • Infinites outside of math?
    The number 0 is not a riddle.TonesInDeepFreeze

    But if you say it's the number of times you can map it on R it is. I can even map a single element of N to R.
  • Infinites outside of math?


    I looked it up when I wrote about the alephs, and it was even the reason for my post. Seems years ago.
  • Infinites outside of math?
    So what? This is not a game with a scoreboard for how many questions I've answered.TonesInDeepFreeze

    Who says it is? I just said you have answered with a riddle.
  • Infinites outside of math?
    So years ago you looked it up, but still don't understand it now.TonesInDeepFreeze

    I don't mean that litteraly.
  • Infinites outside of math?
    I can map N infinite times infinite times on R.
  • Infinites outside of math?
    I really would rather not know about the bedtimes of you and your wife.TonesInDeepFreeze

    Then ignore it. The only riddle you gave as an actual answer is that you can map N zero times on R.
  • Infinites outside of math?
    I'm not surprised that your attention span wouldn't provide recalling my question: Why won't you look up 'continuum hypothesis' on the Internet?TonesInDeepFreeze

    I have done that years ago already. I don't agree though. I'm not a parrot like you.
  • Infinites outside of math?
    Liza is getting tired and reduced to token replies.TonesInDeepFreeze

    Now you take refugee behind empty verbiage. Liza is tired indeed. My wife lies in bed for a couple of hours already... I told her to come too. Three hours ago...
  • Infinites outside of math?
    That you don't understand the answer is not my problem. I did answer it. Now your turn to answer my question,.TonesInDeepFreeze

    That's no answer why it's false. You seriously believe you can map N zero times on R? What's your question?
  • Infinites outside of math?
    The claim you made, as I quoted it, silly.TonesInDeepFreeze

    But why false?
  • Infinites outside of math?
    Do you mean N onto R?

    The answer is 0.
    TonesInDeepFreeze

    Ah, I didn't see that one! 0 times? Are you kidding?
  • Infinites outside of math?
    Not the zillionth time, but it is the second time you have made that false claim.TonesInDeepFreeze

    Then what is false?
  • Infinites outside of math?
    No one ever told you that mathematics is not throwing around words like 'conformal' while not knowing what they mean'.TonesInDeepFreeze

    Everyone knows what conformal means.
  • Infinites outside of math?
    I answered one of your questions.TonesInDeepFreeze

    You haven't answered one!
  • Infinites outside of math?
    You don't know what you're doingTonesInDeepFreeze

    Yeah, that's the zillionth time you mentioned this. I haven't seen one thing to conclude you do. You only make references.
  • Infinites outside of math?
    That is purely arbitrary unfounded assertion.TonesInDeepFreeze

    If you consider the infinite line the discrete elements on the plane, like the natural numbers on R, than the relation between the lines and RxR, the infinite plane, is conformal to the relation between N and R.
  • Infinites outside of math?
    You contradict yourself. You claim there is a bijection from N onto R, but above you admit that the interval [0 1] is uncountable.TonesInDeepFreeze

    You have to read what I write. There are infinite bijections between between N and [0-1]. Like there are an infinite times infinite between N and R. And there are an infinite times infinite between R and RxR.
  • Infinites outside of math?
    Wrong. For any infinite set S.TonesInDeepFreeze

    And that's exactly where the failure lies. The relation between R and RxR is the same as the relation between R and N. R can be viewed as corresponding so a single cardinal. How many lines you need to construct RxR? The same number as the number of cardinals to construct R.
  • Infinites outside of math?
    It's not so complicated as they make it. There are basically two types of infinities. Infinite countable infinities, like N and infinite times infinite types. Like the interval [0-1]. Uncountable. All alephs are multiplicities of them.
  • Infinites outside of math?
    I have been referencing the more general theorem that for an infinite set S and natural number n>0, we have card(S) = card(S^n).TonesInDeepFreeze

    That's for countable sets. For R this doesn't hold.
  • Infinites outside of math?
    I just asked you the question how many times you can map N on R.
  • How Useful is the Concept of 'Qualia'?


    How can his network be different if he believes the door is open? Is he lying? Have we wrongly identified his network? If he's not lying then his believe part should be the same.
  • How Useful is the Concept of 'Qualia'?
    If we examine person 1001, who claims to believe that the door is open, and do not find in them that specific neural network, do we conclude that we have not identified the correct specific network, or do we conclude that they do not really believe the door is open?Banno

    Are the other 1000 all the same, under the same conditions? If he believes the door is open, why should his network be different? Is he lying?
  • How Useful is the Concept of 'Qualia'?
    Sorry, I don't know what you're sayingfrank

    Ecactly what I wrote. It's plain English. You can exclude the worm and still see it with closed eyes and imagination.
  • Infinites outside of math?


    Okay, N^2, as you wish. Same as inf^2.
  • Infinites outside of math?


    Show the correct answer then. I already gave you a link to a supposed bijection between R and RxR. How many times can N be mapped on the real line? Just offer a tasty recipe.

AgentTangarine

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