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Set Theory Beginner

  1. Jun 12, 2013 #1
    Gentlemen,

    I am writing to you in order to identify an idea I have and to see how this idea can be mathematically expressed. My understanding is that this idea pertains to Set Theory and I am going to do my best in expressing this idea for you-

    x y z are formed into two sets, x|y and y|z.

    The elements which compose x y z are the same for each ranging from ( 1-9 ).

    The combination of any two of these numbers will result in a set value, meaning that 9|1 can equal to 8.5 and 1|7 equal to 2.3.

    The set value reference chart varies and is currently not defined. However, it does range from 1|1.0 to 9|9.9.

    Now this would form a new set. Hence the result of x|y is A and y|z is B. These would then provide a new set, resulting in a new set value. The way I work this in this idea, is that Integers are split from the decimal value and joined with the decimal values summed, i.e., 8|2.8 which then has a set value of 5.4. So in the end x | y | z ( 9 | 1 | 7 ) is equal to 5.4. C=5.4.

    How do I write this, in an elegant mathematical expression?

    Thank you for your consideration and input, regarding this idea.

    Someone with an idea...
     
  2. jcsd
  3. Jun 12, 2013 #2

    Mark44

    Staff: Mentor

    The usual notation for a set involves braces - {}.
    You have a set: {x, y, z}.
    You form two subsets: {x, y} and {y, z}.

    Are what you are calling sets actually ordered pairs of numbers? I can write {1, 2, 3} as a set. Using your notation, does 1|2|3 make sense or can there be only two things in the sets?

    Are the values of x, y, and z the integers from 1 through 9 or do they also include all of the real numbers in this interval?
    How are these values obtained?
    If it's not defined, why talk about it? What is the purpose of a "set value reference" chart?
    What do 1|1.0 and 9|9.0 mean?
    You need to explain this better. How does 8|2.8 (whatever that means) result in 5.4?
    How does (9 | 1 | 7) result in 5.4? What is C?
     
  4. Jun 13, 2013 #3
    Mark44,

    Thank you for your feedback and questions; I will attempt to answer these in the order received.

    Background. I have no mathematics background but was always fascinated with numbers and I have been putting this idea together for the past 12 years and have reached a point where I would like to understand what it is that I have here and obviously present it to a mathematical community of experts in an elegant mathematical expression. So with that said...

    {x,y,z}
    {x,y} and {y,z}

    If ordered pairs are 11, 12, 13... meaning that the elements that make up x,y,z are from the same pool of numbers ( 1,2,3,4,5,6,7,8,9 ); then yes. Which in the example I provided x=9, y=1, z=7. Then the ordered pairs would be 91 and 17 for {x,y} and {y,z}.

    Now the ref. chart takes the ordered pair and compares it to a changing value also ( 1 through 9 ) however broken down with decimal values. Meaning that 91 would be equal to 8.5 and 17 would equal 2.3 in accordance to the reference chart.

    This is why I mentioned the reference chart, because it is part of the element that goes in to the second part. The second part is where the 8.5 and 2.3 results are combined into a new ordered pair which I called {A,B} the result of {x,y} and {y,z}. The way they are combined is by taking the integers 8 and 2 which become 82 and summing the decimals .8, resulting in 82.8.

    This 82.8 is then ref. the above mentioned chart and the associated value could be 5.4.

    I called the result "C" for this forum, hence C=5.4.

    The chart is constantly changing and is extremely long and in many ways irrelevant. I just wanted to inform that the results are obtained from a relevant source used in the second part and which provides the end result.

    However, the ref chart is structured as such, example...

    11.0 = 1.0
    11.1 = 1.02
    17.0 = 2.30
    --break--
    31.0 = 4.0
    32.1 = 4.22
    --break--
    82.8 = 5.43 rounded 5.4
    --break--
    91.0 = 8.5
    99.9 = 9
    etc, etc, etc... (11.0 ~ 99.9)

    Ok so how are values obtained. Mike44, {x,y,z} are three distinct and independent mechanisms which are paired up are then to an ever changing ref. chart. The fact that these are structured the way they are {x,y,z} is based on a priority. An ever changing priority which based on multiple variables/elements influenced by an erratic dynamic population.

    Now I will say that I am being somewhat obscure with purpose. But the basic and most important element/idea I am trying to convey are presented here without outlining those areas which may lean on proprietary.

    Hope the above makes sense.

    U_Unk.
     
    Last edited: Jun 13, 2013
  5. Jun 13, 2013 #4

    Mark44

    Staff: Mentor

    There needs to be a separator between the things in an ordered pair. Points in the plane are identified by ordered pairs such as (2, 1). The graph of a function consists of a set of ordered pairs (x, y), where there is a particular kind of relationship between the first number in the pair and the second number.

    Your ordered pairs above should be written as (9, 1) and (1, 7).
    "Equal" is not the right word. 91 is NOT equal to 8.5, nor is (9, 1) equal to 8.5. Better choices would be "maps to" or "corresponds to." You could even use an arrow to show this relationship, as below:

    (9, 1) → 8.5
    (1, 7) → 2.3

    It's not stated how this mapping works, but that's not important. Apparently, you read from the "9" row and the "1" column in the lookup table to get the value at this location.


    OK, I follow this, but it could be stated more clearly.

    Starting with 8.5 and 2.3, we do the following:
    1. Form the ordered pair (8, 2) from the integer parts of 8.5 and 2.3
    2. Combine the fractional parts of 8.5 and 2.3 (.5 and .3) to .8.

    At this point the ordered pair business breaks down, since the result from above would have to be written as (8, 2).8 .

    Maybe it's something like this, again starting with 8.5 and 2.3:
    1. Extract the integer parts of 8.5 and 2.3 to get 8 and 2.
    2. Form the number 10*8 + 2 = 82
    3. Add the fractional parts (.5 + .3 = .8)
    4. Add the result from the previous step to the number in step 2, resulting in 82.8.

    Is this what you're doing?



    I don't follow this, probably because I don't understand how the chart works.
    This is a simpler chart that what I was imagining. What you have here is a mapping between the interval [11.0, 99.9] and the interval [1.00, 9.00]. The numbers in the first interval are in increments of 0.1 (it seems).
     
  6. Jun 14, 2013 #5
    Mark44,

    I think I am grasping this from this end.

    So, let's see if I understand this.

    (x,y) and (y,x) are-

    (x,y) → ref
    (y,z) → ref​

    Now this 'map to', 'corresponds to', or ' → ' then becomes (A,B), meaning the result of (x,y) → ? would be (x,y) → A and (y,z) → B, which then becomes (A,B) → ref, or in my case, (A,B) → C. Am I on the correct path?

    Because if I added values it would then be-

    (9,1) → 8.5
    (1,7) → 2.3
    10*8 + 2 = 82
    (.5 + .3) = .8
    82 + .8 = 82.8 which actually is (8,2).8 (?)
    (8,2).8 → 5.4​

    Regarding the chart.

    Ok. Starting from the lowest element [11.0] through the highest [99.9], certain areas will fluctuate, except for the highest and the lowest. Meaning that [11.0] will always be equal to 1.0 and [99.9] will always be equal to 9.0. Now certain elements in between will vary at times, meaning that 31 at time maybe higher than 13 and vice-versa. So, depending where they fall in priority, the entire spread of combinations without decimals, will depend on their ranking from 1 through 9. So [11.0 through 11.9] will always be the lowest, [99.0 through 99.9] will always be the highest.

    Further elaboration regarding the chart regarding the decimals and how values are obtained.

    Well the chart is a bi-product of conversion/scaling equation. We take the new established order from [11.0 through 99.9] and just match it up accordingly to a [1.0 through 9.0] conversion.

    The way we are converting/scaling is -

    OldRange = (OldMax - OldMin)
    NewRange = (NewMax - NewMin)
    NewValue = (((OldValue - OldMin) / OldRange) * NewRange) + NewMin​

    However we are not using the 11.0 through 99.9 values to convert over but rather using the ranking value 1- 890; we use the ranking value since the mid range is constantly fluctuates.

    So it looks like this in excel:
    [ (((Ov-Om)/Or)*Nr)+Nm ] = Nv "Rounded to the third decimal point"
    [ (((1-1)/889)*8)+1 ] = 1.000
    [ (((99-1)/889)*8)+1 ] = 1.882
    [ (((275-1)/889)*8)+1 ] = 3.466
    etc, etc.​

    Example-
    Rank ____ Ref ____ Value
    1 ______ 11.0 ____ 1.000
    99 _____ 20.8 ____ 1.882
    275 ____ 38.4 ____ 3.466​

    The Ref values- [11.0], [20.8], & [38.4] derived from: (x,y) or (y,z) or (A,B) with the output being the Value Column.​


    Mark44,

    Again I want to thank you for taking the time to assist me in this. I am greatly appreciative and thankful for your input, greatly!

    R/S

    U_Unk
     
    Last edited: Jun 14, 2013
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