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Thread: "warning speculation" Relative Mathematics

  1. #46
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    Re: "warning speculation" Relative Mathematics

    I am sorry I should have written extensive and intensive properties.
    That is quite different.

    my mistake.

    No I am not checking equations for correctness, I can't because I don't understand your rules of arithmetic.

    Do you know how many axioms there are in Euclid?

    Only 5

    So people often say that Euclidian Geometry is built on five axioms.

    This is only a partial truth since those 5 axioms are supported by 23 definitions and a further 5 'common notions', effectively making 33 statements of axiomatic status in all.

    I don't know what your equivalent support statements are so I would be in serious danger of mis-stepping.

    Equally I can't see what you mean by your definition of infinity. (you have posted a great deal of text after all).
    So please just quote it or something so it can be found.
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  2. #47
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    Re: "warning speculation" Relative Mathematics

    Thank you,

    Only two axioms are discarded. All other axioms are kept.

    1. Zero product property
    2. Division by zero undefined.

    There are four kinds of numbers.

    1 Undefined = ( undefined value, undefined space )
    2 Relatives = ( defined value, undefined space )
    3 Zero = 0 = ( undefined value, defined space )
    4 Defined Numbers = ( defined value, defined space )

    It is then that the process of "further defining" structures the finites and infinites with any number composing ( Dv + Ds ).

    7infinte = ( 7 defined values infinite large + 7 defined spaces infinite large ) = ( 7dvIl + 7dsIl )
    .7infinite = ( 7 defined values infinite small + 7 defined spaces infinite small ) = ( 7dvIs + 7dsIs )

    So then it is these specific "number" representations for "space" and "value" that are applied when * or / by any kind of number.
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  3. #48
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    Re: "warning speculation" Relative Mathematics

    I will deal with both what I have offered and what you have proposed.

    First one classification of properties is to divide them into extensive and intensive properties.

    Extensive properties are cumulative.
    The values for each small part of the whole add up to a cumulative sum for the entire body or system.
    That is they depend upon space (perhaps like your idea).
    Examples are mass and volume.
    So the bigger the brick the more volume it occupies and the more mass it has.

    These are perhaps a bit like you number and space idea.

    Intensive properties are not cumulative.
    The property value for a small part of the whole is the same as the property value for the whole body or system.
    Examples are pressure and temperature.
    At equilibrium it doesn't matter if we take a small part of a balloon of gas or the whole balloon of gas, the temperature and pressure are the same.

    Secondly my short list of questions that you did not attempt.

    What is the property of a cold/hot reservoir that makes it so?
    What is the property of an electrical earth that makes it an electrical earth?
    What does infinite dilution mean in chemistry?
    If you inflate a balloon in the atmosphere, how does that affect does the volume and pressure of the atmosphere?
    A hot or cold reservoir does not alter in temperature no matter how much heat you take out or add.

    An electrical earth is a one terminal component or device that does not change in electrical potential no matter how much current (charge) it sources or sinks.

    Infinite dilution is the chemical concentration beyond which the rate and other important reaction paameters are unaffected.
    It is an asymptotic intercept on the concentration axis of the graph of some property plotted against concentration (or dilution).

    If you inflate a balloon in the atmosphere, neither the pressure nor the volume of the atmosphere change.


    Hopefully you can see the trend, and why I have introduced these subjects, there are many, many more instances of such models in applied mathematics.


    Now to your last post.

    I am an applied mathematician, not a pure mathematician so what follows is an applied (get things done) mathematician's rough and ready guide to axiomatic systems.

    Only two axioms are discarded. All other axioms are kept.

    1. Zero product property
    2. Division by zero undefined.
    Neither of these qualify for the status axiom. Nor are they complete enough to be used as a definition.

    Your attempt at an axiomatic system follows Euclidís method, but Iím sorry to tell you not successfully.

    Before you can state axioms you need to state definitions.

    Your sequence of statements should be such that they are not circular. That is they only rely on previous statements and do not rely on something that is introduced later.

    So you cannot have this without defining infinity.

    7infinte = ( 7 defined values infinite large + 7 defined spaces infinite large ) = ( 7dvIl + 7dsIl )
    You have also introduced a difficulty here since you are using the + symbol to mean two different things

    It is then that the process of "further defining" structures the finites and infinites with any number composing ( Dv + Ds ).
    So read Euclid
    Then start at the beginning.
    Define something.
    Postulate an axiom concerning it
    Deduce some properties as a result of the axiom and the definition.
    Repeat.

    Modern mathematics follows a different route via set theory.
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  4. #49
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    Re: "warning speculation" Relative Mathematics

    What is the property of a cold/hot reservoir that makes it so?.....This is not to say that the "heat" ceases to exist. Nor is the "heat" undefined. No loss of heat actually occurs.
    What is the property of an electrical earth that makes it an electrical earth?....This is not to say that the "electrical energy" is lost. It is always there and measurable. Just no longer with in the electrical earth.
    What does infinite dilution mean in chemistry?....This is not to say that the molecules of the "thing" being added cease to exist when added to the solution. They are always there, just no longer measurable from the perspective of "ratio" towards the rest of the solution.
    If you inflate a balloon in the atmosphere, how does that affect does the volume and pressure of the atmosphere?.....This is not to say that pressured gasses are not added to the balloon, ergo atmosphere, It is only that from the perspective of the atmosphere no pressure was altered. Cleary atoms were added.

    These are in reference to division by zero correct? The thing is, as an applied mathematician should now. Nothing ever disappears, nor does anything ever become "undefined". It is only that it appears so to us.

    What definitions would you like from me.

    value= labeling of quantities of existence, other than dimensions.
    space= labeling of quantities of dimensions.

    There is nothing wrong in stating that all current axioms are the same. That is the word "infinite" is axiomatically defined by the likes of Cantor and so forth. I change nothing in these regards. So then if you want a definition of infinity, not merely a representation of how I use it, then use the one you already know. I see nothing to change in this regard. All I am changing is how numbers are perceived and defined. As well as how they operate in regards to * and /. Really I do not think I am changing anything. Only more accurately describing what and how it works.

    Lastly...granted I may not follow in suit of current "written paradigms". But this is not necessary. All that is, is finding a flaw within the ideas. I may state these ideas however I wish.

    I also gave definitions for * and /. I can re post if you care. So then what further definitions are necessary from me?
    Last edited by Conway; Jun 23rd 2015 at 02:36 PM.
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  5. #50
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    Re: "warning speculation" Relative Mathematics

    I may state these ideas however I wish.
    Yes you may certainly do whatever you wish.

    But since you are playing games and wasting my time I am calling a halt and wish you adieu.
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  6. #51
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    Re: "warning speculation" Relative Mathematics

    My apologies, this was not the intention. That statement was only to say, that I do not necessarily have to write like "academia" demands. Truly....thank you for your time.
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  7. #52
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    Re: "warning speculation" Relative Mathematics

    It would help if you would at least write intelligibly- so that we could understand what you are trying to say!
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  8. #53
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    Re: "warning speculation" Relative Mathematics

    Halls, have you been trying to understand his stuff since Jun 23rd (last post)?
    And have given up only today?
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  9. #54
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    Re: "warning speculation" Relative Mathematics

    Lol?.....maybe this will help Hallsofivy.....



    For every A in S there exist a Z1 and a Z2, such that any A in operation of multiplication is only representing Z1 or Z2 in any given equation. Allowing that Z1 for zero equals 0, and Z2 for zero equals 1.


    Also

    Space and Time is dictated by our perspective of the "body of reference".

    The sum of multiplication and division is dictated by our perspective of "space and value".


    Also

    Zero used as an exponent is zero as space.
    Zero used as a logarithm is zero as value.
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  10. #55
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    Re: "warning speculation" Relative Mathematics

    Mrs Pi : oh boy, my husband is soooo irrational...
    and the sob never stops playing the numbers...
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  11. #56
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    Re: "warning speculation" Relative Mathematics

    I think this thread has got about as far as it's going to go.

    Thread closed.

    -Dan
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