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Infinity

I am not a mathematician, nor a scientist, hell, I'm not even a Lutheran. In fact, I am an artist...only because what I do is not anything else. Nevertheless, this notion appeared in my thoughts as I awoke one morning, I apologize for my ignorance, but, here it is: ∞ + 1 = ∞

I'm pretty sure it is nonsense. I, however, would appreciate comments and your thoughts.

Comments

  • 1.
    edited July 2013

    We need art for the project, or was that the extent of your interest :D

    Comment Source:We need art for the project, or was that the extent of your interest :D
  • 2.
    edited July 2013
    No. Just the odd equation that happened. I know it is absurd, but... I think this has more to do with intuitive sense, more than mathematics or science...although intuitive insights are common to both art and science. I was hoping for some understanding of the equation in conventional terms.
    Comment Source:No. Just the odd equation that happened. I know it is absurd, but... I think this has more to do with intuitive sense, more than mathematics or science...although intuitive insights are common to both art and science. I was hoping for some understanding of the equation in conventional terms.
  • 3.
    edited July 2013

    You'll find more details on this wikipedia page but in the most common way of modelling things, basically $\infty + 1 \ne \infty$, but you do have that $1+\infty = \infty$... I'd love to spend more time discussing this, but unfortunately I'm already behind on my contribution to a paper...

    (Edit: the "most common way of modelling" above was an attempt to avoid having to talk about the distinction between ordinal and cardinal infinities. The above is in terms of ordinals, and the non-commutativity of ordinal transfinite addition might have been intriguing and make readers want to find out more about the weird world. Todd has a great explanation about cardinal infinities below.)

    As Jacob says, Azimuth could definitely do with some interesting art.

    Comment Source:You'll find more details [on this wikipedia page](http://en.wikipedia.org/wiki/Ordinal_arithmetic) but in the most common way of modelling things, basically $\infty + 1 \ne \infty$, but you do have that $1+\infty = \infty$... I'd love to spend more time discussing this, but unfortunately I'm already behind on my contribution to a paper... (Edit: the "most common way of modelling" above was an attempt to avoid having to talk about the distinction between ordinal and cardinal infinities. The above is in terms of ordinals, and the non-commutativity of ordinal transfinite addition might have been intriguing and make readers want to find out more about the weird world. Todd has a great explanation about cardinal infinities below.) As Jacob says, Azimuth could definitely do with some interesting art.
  • 4.
    All of my art for the past four years is digital and can be found on my Facebook site: R Henry Nigl, there are some 2500 images 'abstractions' there open to the public, additionally, another 3000 images called 'FACES' available only to friends...all are freely available, that is free without cost for non-commercial use...attribution is necessary for all media presentation, Creative Commons licenses apply. Take your pick, let me know if you wish to download.

    Thank you for your input regarding the equation.
    Comment Source:All of my art for the past four years is digital and can be found on my Facebook site: R Henry Nigl, there are some 2500 images 'abstractions' there open to the public, additionally, another 3000 images called 'FACES' available only to friends...all are freely available, that is free without cost for non-commercial use...attribution is necessary for all media presentation, Creative Commons licenses apply. Take your pick, let me know if you wish to download. Thank you for your input regarding the equation.
  • 5.
    edited July 2013

    In cardinal arithmetic, $\infty + 1 = \infty$, and this is pretty much the defining characteristic of infinite things. So your morning thought is not at all nonsense, not at all! But perhaps even more amazing is that there are distinct degrees of infinity in cardinal arithmetic: the infinity of real numbers is provably greater than the infinity of natural numbers. When I first learned this, I thought it was the most extraordinary thing...

    There's a television commercial currently playing in the US (I think for AT&T) which I almost invariably find delightful: a man is seated at a table with a group of young children and asks them what is the biggest number they can think of. The first girl says, "a billion trillion zillion!", and the man says, "That's pretty big" and (turning to the next child), "how about you?"

    -- "Ten".

    -- "Okay... How about you?"

    -- "Infinity!"

    -- (To the next child) "Can you top that?"

    -- "Infinity and one!"

    -- "Actually, we were looking for infinity plus infinity. Sorry."

    -- (The first girl) "What about infinity times infinity?!"

    And the man makes a gesture which says, "you just blew my mind", followed by the voiceover narrating "It's not complicated..." Every time the commercial comes on, I have to suppress a small urge to explain to my kids the distinction between ordinals and cardinals. :-)

    Comment Source:In cardinal arithmetic, $\infty + 1 = \infty$, and this is pretty much the defining characteristic of infinite things. So your morning thought is not at all nonsense, not at all! But perhaps even more amazing is that there are distinct degrees of infinity in cardinal arithmetic: the infinity of real numbers is provably greater than the infinity of natural numbers. When I first learned this, I thought it was the most extraordinary thing... There's a television commercial currently playing in the US (I think for AT&T) which I almost invariably find delightful: a man is seated at a table with a group of young children and asks them what is the biggest number they can think of. The first girl says, "a billion trillion zillion!", and the man says, "That's pretty big" and (turning to the next child), "how about you?" -- "Ten". -- "Okay... How about you?" -- "Infinity!" -- (To the next child) "Can you top that?" -- "Infinity and one!" -- "Actually, we were looking for infinity plus infinity. Sorry." -- (The first girl) "What about infinity _times_ infinity?!" And the man makes a gesture which says, "you just blew my mind", followed by the voiceover narrating "It's not complicated..." Every time the commercial comes on, I have to suppress a small urge to explain to my kids the distinction between ordinals and cardinals. :-)
  • 6.
    edited July 2013

    Maybe you should just say "Pfft, he doesn't know about ordinals versus cardinals!" Thus planting a seed of curiosity (if done right). But you've probably realized you need to resist most of those urges to explain math... since I'm not a parent, I haven't learned that skill. Well, except for my wife.

    Comment Source:Maybe you should just say "Pfft, he doesn't know about ordinals versus cardinals!" Thus planting a seed of curiosity (if done right). But you've probably realized you need to resist most of those urges to explain math... since I'm not a parent, I haven't learned that skill. Well, except for my wife.
  • 7.
    edited July 2013
    Thanks John...But the Wikipedia entries for 'ordinals' and 'cardinals' gave a pretty good overview...not something I read daily, but I do have some understanding of what is going on here. Why would you discourage explanation? I have many other questions relevant to my personal curiosities involving natural and synthetic systems and formulations
    BTW, I am seventy years old...not exactly a child...as your post might suggest to some.
    Comment Source:Thanks John...But the Wikipedia entries for 'ordinals' and 'cardinals' gave a pretty good overview...not something I read daily, but I do have some understanding of what is going on here. Why would you discourage explanation? I have many other questions relevant to my personal curiosities involving natural and synthetic systems and formulations BTW, I am seventy years old...not exactly a child...as your post might suggest to some.
  • 8.
    I suspect ∞ is a nominal number, just a name, and does not exist as either a cardinal or ordinal number in space-time. However, without 'space' and 'time', 'infinity' would be easily perceived...even understood, as a fish understands water.
    Comment Source:I suspect ∞ is a nominal number, just a name, and does not exist as either a cardinal or ordinal number in space-time. However, without 'space' and 'time', 'infinity' would be easily perceived...even understood, as a fish understands water.
  • 9.
    I have always considered 'infinity' as a simple identification that with efforts to describe mathematically seem to be about as perplexing as the 'Ship of Thebes Paradox' and of course any paradox, the study of which can be most frustrating and treacherous when treating a paradox, and thus 'infinity', as a number. Regarding the 'Ship of Thebes' paradox: it, the 'ship' always remains the same identity, no matter how many planks are changed or even if totally rebuilt, it will always be called 'The Ship of Thebes'.

    In the end I arrived at the notion, for myself at least, that the perception of 'paradox' is keyed to movement in space and thus time, thus, as all things concrete and all of consciousness, being in constant motion through space-time, so to is 'paradox', it is essentially language non-sense and so too is 'infinity'.

    To illustrate, 'infinity' as a 'number' used in any way other than as a simple identifier, that is as a symbol, results in a paradox.

    As in classic and modern mind-body problems 'infinity' resolves itself as we 'move' toward or away from it, or simply thinking about it, only coming into existence as a result of our movement and consciousness. Otherwise, it, 'infinity' does not exist. (That's a poor description, and enters the realm of theology and metaphysics...but, is reflective in a general way of what I am thinking.)
    Comment Source:I have always considered 'infinity' as a simple identification that with efforts to describe mathematically seem to be about as perplexing as the 'Ship of Thebes Paradox' and of course any paradox, the study of which can be most frustrating and treacherous when treating a paradox, and thus 'infinity', as a number. Regarding the 'Ship of Thebes' paradox: it, the 'ship' always remains the same identity, no matter how many planks are changed or even if totally rebuilt, it will always be called 'The Ship of Thebes'. In the end I arrived at the notion, for myself at least, that the perception of 'paradox' is keyed to movement in space and thus time, thus, as all things concrete and all of consciousness, being in constant motion through space-time, so to is 'paradox', it is essentially language non-sense and so too is 'infinity'. To illustrate, 'infinity' as a 'number' used in any way other than as a simple identifier, that is as a symbol, results in a paradox. As in classic and modern mind-body problems 'infinity' resolves itself as we 'move' toward or away from it, or simply thinking about it, only coming into existence as a result of our movement and consciousness. Otherwise, it, 'infinity' does not exist. (That's a poor description, and enters the realm of theology and metaphysics...but, is reflective in a general way of what I am thinking.)
  • 10.

    I hope you understand that this discussion is not relevant to the main aims of the Azimuth Project, which are listed here.

    Comment Source:I hope you understand that this discussion is not relevant to the main aims of the Azimuth Project, which are listed [here](http://www.azimuthproject.org/azimuth/show/HomePage).
  • 11.
    I reviewed several Forum discussions and believed it conformed, I have read the mission guidelines and may have misunderstood those aims...it seemed topics were all over the place. In any event I am happy for the input I received.
    Comment Source:I reviewed several Forum discussions and believed it conformed, I have read the mission guidelines and may have misunderstood those aims...it seemed topics were all over the place. In any event I am happy for the input I received.
  • 12.

    The Azimuth Forum is about environmental problem - and mathematics, science and engineering that might help solve those problems.

    Comment Source:The Azimuth Forum is about environmental problem - and mathematics, science and engineering that might help solve those problems.
  • 13.
    edited July 2013
    Got it, John...thank you greatly...it's not a problem, just a misunderstanding on my part, I've been a fan of yours for years and honored to be able to access this site...I think I started reading your posts actually way back when the internet was just text, I dunno when that was...but you maintained a mathematics forum bulletin board, even then (how do you find the time?)...my commercial background (re. how I maintained income over the years) is in architectural design, advertising and marketing...mathematics, especially the history and philosophy of, is for me simply a 'hobby'. Thank you.
    Comment Source:Got it, John...thank you greatly...it's not a problem, just a misunderstanding on my part, I've been a fan of yours for years and honored to be able to access this site...I think I started reading your posts actually way back when the internet was just text, I dunno when that was...but you maintained a mathematics forum bulletin board, even then (how do you find the time?)...my commercial background (re. how I maintained income over the years) is in architectural design, advertising and marketing...mathematics, especially the history and philosophy of, is for me simply a 'hobby'. Thank you.
  • 14.
    edited July 2013

    Okay, no problemo. I started running "sci.physics.research" sometime around 1993, I think.

    Comment Source:Okay, no problemo. I started running "sci.physics.research" sometime around 1993, I think.
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