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1 = 2.

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  • Registered Users Posts: 1,328 ✭✭✭Sev


    All I said, is that an infinite tactile quantity cannot exist. Which is obviously true.
    The question of whether 0 is the smallest number that can exist is actually an good example of how such things can be confusing. Bard claims that negative numbers are smaller, which is correct if you take a set such as the integers or the reals and the operation < (less than), but you then correct him and reveal that you're actually using a different set of goalposts (the set of natural numbers, or non-negative reals or some such, who knows).

    Thankyou for just reiterrating the point Ive been trying to get across this entire thread.
    Originally posted by ecksor
    Anyway, I don't think this a useful discussion to continue.

    As I said.


  • Moderators, Social & Fun Moderators Posts: 10,501 Mod ✭✭✭✭ecksor


    Originally posted by Sev
    Thankyou for just reiterrating the point Ive been trying to get across this entire thread.

    :rolleyes:

    I find that ironic, since the point I was trying to make is that you're not defining the context in which your speaking in a way that makes the contentious statements you've made make any sense.

    Yes, I appreciate that "it depends on context" was one of your points, but you made some very definite assertions about what infinity is that you didn't make any attempt to qualify by providing ANY context in which what you claim (that infinity is a number) makes any sense. I'd settle for just one, since if you could provide one it would be something interesting that I haven't come across before.

    I know I said I didn't want to continue this, but I find it immensely frustrating when people continue to post "no, that's not what I'm talking about. no, that's not what I'm talking about either", since I never know if there is an interesting point that I'm missing or not. If this doesn't have anything to do with maths, then just come out and say so (although how you can attempt to resolve something like infinity or, more importantly, why you would want to would be an interesting discussion in itself).


  • Registered Users Posts: 1,328 ✭✭✭Sev


    Well I apologise for any confusion, I would have thought the majority would understand my point of view instead of doing everything they can to find faults (that are completely subjective) with everything I say. Yes, most of everything I have said is based on perfect common sense and logic. I am just trying to separate standardised abstract mathematical axioms from practical understanding.

    You are trying to strictly quantify and qualify everything I say. My point is that the maths is entirely subjective. Yes, infinity can be a number if I want it to be. I find no difficulty in contemplating a number which is infinitely big, whether "technically" that does not constitute the expression of infinity in the way that official international mathematical standards defines makes no odds to me. Although you seem quite hung up on that.

    Mathematics at its heart is simply a tool, a way of simulating or predicting physical events by the application of logic. I just take exception to the strict definitions or governing rules that only have any relevance in an entirely non physical situation.

    If I asked you, what is a number that is bigger than any other number? you would tell me infinity, or that no such number exists.


  • Moderators, Social & Fun Moderators Posts: 10,501 Mod ✭✭✭✭ecksor


    Originally posted by Sev
    Well I apologise for any confusion, I would have thought the majority would understand my point of view instead of doing everything they can to find faults (that are completely subjective) with everything I say.

    I'm not the majority, I tend to take a purely math based view of such things. If it looks like I'm nitpicking, it's because I am nitpicking, but the difference is that I think such things are important, and you don't, which is fair enough, I now understand your point of view.
    You are trying to strictly quantify and qualify everything I say. My point is that the maths is entirely subjective.

    mathematics is not subjective. It is a means to express and reason about concepts in a formal and objective manner.

    I find no difficulty in contemplating a number which is infinitely big, whether "technically" that does not constitute the expression of infinity in the way that official international mathematical standards defines makes no odds to me. Although you seem quite hung up on that.

    This is a hang up? Good grief, I had no idea. The word 'standard' makes it sound like infinity is overseen by a committee :D
    Mathematics at its heart is simply a tool, a way of simulating or predicting physical events by the application of logic. I just take exception to the strict definitions or governing rules that only have any relevance in an entirely non physical situation.

    It can be a tool that is applied, or a purely abstract thing. However, I'm not sure it does much good in either case if it does not demand rigour, which was what I was looking for.
    If I asked you, what is a number that is bigger than any other number? you would tell me infinity, or that no such number exists.

    I'd probably say that no such number exists. Then again, it might depend on how you frame the question or what set we're talking about in other words. Mathematics has the notion of the well-ordering principle that states that if a set has at least one member, then it has a least member. There is no equivilent for a greatest member, for obvious reasons.


  • Business & Finance Moderators, Entertainment Moderators Posts: 32,387 Mod ✭✭✭✭DeVore


    Originally posted by Sev
    I am just trying to separate standardised abstract mathematical axioms from practical understanding.


    I cant imagine why...

    You are trying to strictly quantify and qualify everything I say. My point is that the maths is entirely subjective. Yes, infinity can be a number if I want it to be. I find no difficulty in contemplating a number which is infinitely big, whether "technically" that does not constitute the expression of infinity in the way that official international mathematical standards defines makes no odds to me. Although you seem quite hung up on that.

    Details are important in mathematics. You are of course quite free to imagine infinity as a "giant pink elephant" in your "subjectivity" but then you are breaking from the correct usage of the mathematical term. If thats what you are doing then I consider you a fwthong[1].


    Mathematics at its heart is simply a tool, a way of simulating or predicting physical events by the application of logic. I just take exception to the strict definitions or governing rules that only have any relevance in an entirely non physical situation.

    Because 1 apple and 1 apple doesnt make 2 apples?


    requoted from above:
    My point is that the maths is entirely subjective.

    Um no its not, in fact one of the most important things that a mathematician strives for is to remove subjectivity from his/her logic.

    2+2=4 regardless of how you define terms. We commonly agree these "gutteral tones" to convey mental images but beyond that the mathematics of that equation are ALWAYS TRUE.

    I cant wander around believing that for me 2+2=5 ... well I can, I'm just wrong.

    Now, what I CAN DO is redefine my notation so that *I'm* using the symbol "5" to mean what the rest of you refer to as "4". If I do that then 2+2 DOES equal 5 under my notation.

    That, however, is not subjectivity. The notation may change but the logic doesnt.

    DeV.

    [1] I will define "fwthong" however I see fit :p


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  • Registered Users Posts: 1,328 ✭✭✭Sev


    I didnt say that maths is entirely subjective, I said that 'the' maths was entirely subjective: the aforementioned very abstract and particular 'laws' regarding infinity. Notice the subjective use of the word the :)

    As for the point im trying to make, which I still havnt seemed to convey, is that the concept of mathematics I perceive, is not based on rules, rigour or standardised doctrine. But the fundamental application of logic.
    Details are important in mathematics. You are of course quite free to imagine infinity as a "giant pink elephant" in your "subjectivity" but then you are breaking from the correct usage of the mathematical term.

    But that is exactly what I don't need, "mathematical terms" and "details" if I can visualise, comprehend and achieve a solution with my own understanding of what is going on, without any need to categorise elements of my calculations into 'sets', 'subsets' or whatever jargon you require to reconcile a problem with your notion of mathematics.

    Im going to let this rest now, cos Im finding this extremely difficult to explain and would appear to have a completely distinct and incompatible mindset approaching this whole debate. But I shall continue working with my giant pink elephant.


  • Registered Users Posts: 12,309 ✭✭✭✭Bard


    Ok I take back what I said about negative numbers being "smaller" than 0. They're not, they're just 'lesser'.
    But that is exactly what I don't need, "mathematical terms" and "details"

    Maths is a precise science. It's very important to be precise and stick to specific definitions. That's not to say that you can't use allegories to better explain these definitions... and that's not to say that conventional wisdom cannot be challenged - we'd have no innovation otherwise.

    Infinity is an impractically non-existant number of undefinably massive magnitude. It's what you could imagine getting if you tried dividing anything by zero. I say you "could imagine getting" because there is no possible answer.

    Allegorically here, the question could be posed: "if people were to queue up to get some cake from you and the portion you gave to each person was zero, how many people could you serve?"... there, the answer would be 'infinity'... but technically the answer could be 'it is impossible to answer this question'.


  • Business & Finance Moderators, Entertainment Moderators Posts: 32,387 Mod ✭✭✭✭DeVore


    As for the point im trying to make, which I still havnt seemed to convey, is that the concept of mathematics I perceive, is not based on rules, rigour or standardised doctrine. But the fundamental application of logic.

    Ok, I'm sorry, but that just crashed my brain.

    Russell's Principia Mathematica is a good but weighty read on the topic of mathematics as it corresponds to logic (or rather, vice versa).

    I think I can safely say that most scientists and mathematicians to consider "logic" without "rigour" to be "opinion".

    There is such a thing as fuzzy logic, but theres no such thing as sloppy logic. :)

    DeV.


  • Closed Accounts Posts: 9,314 ✭✭✭Talliesin


    Freedom is the freedom to say 2+2=4. If that is granted, all else follows.
    - George Orwell, 1984


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