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Thread: division

  1. #1 division 
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    what is division?
    1 7
    2 6
    3 5
    4 4
    what is the concept of division?


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  3. #2  
    Forum Masters Degree thyristor's Avatar
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    Division can be seen as repeatedly subtraction of the denominator from the numerator. The result of the operation is how many times you can subtract the denominator from the numerator.


    373 13231-mbm-13231 373
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  4. #3  
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    thyristor, that doesn't help explain (pi+1)/e easily. In general, a/b is defined to be the element x (if it exists) from what ever collection you are working in (groups, rings, graded algebra's etc) such that a = x * b

    So 21/7 = 3 since 21 = 3*7
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  5. #4  
    Forum Masters Degree thyristor's Avatar
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    Sorry, I din't get what he meant by the sequence of numbers.
    373 13231-mbm-13231 373
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  6. #5  
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    No idea either...
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  7. #6  
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    Quote Originally Posted by river_rat
    thyristor, that doesn't help explain (pi+1)/e easily. In general, a/b is defined to be the element x (if it exists) from what ever collection you are working in (groups, rings, graded algebras etc) such that a = x * b

    So 21/7 = 3 since 21 = 3*7
    If it exists, it has to be unique as well – otherwise it’s not defined. 0/0 (in a field) is not defined because it’s not unique: 0 = 0·0 = 1·0.
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  8. #7  
    Forum Professor river_rat's Avatar
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    right and left divisors need not be unique though JaneBennet - you need a cancellation property usually for that to work if i recall.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  9. #8  
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    And the cancellation property fails for 0 in a field because 0 does not have a multiplicative inverse in a field.

    What I’m trying to say is

    a/b is defined to be the element x (if it exists) from what ever collection you are working in (groups, rings, graded algebras etc) such that a = x * b
    if b = 0, you cannot define a/b uniquely this way for the purpose of division. It would mean division by 0.
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  10. #9  
    Forum Professor river_rat's Avatar
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    I was heading more towards semigroups without cancellation where the zero problem explodes
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  11. #10 division 
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    consider the division 7/3. here if we subtract 3 from 7 repeatedly we reach a stage where the denominator is greater than the remainder.i. e. we obtain integers and fractions from division.
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  12. #11  
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    rofl jane bennet gets owned by river_rat every maths thread

    The rat got mad mathematical skills
    everything is mathematical.
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  13. #12  
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    Quote Originally Posted by river_rat
    I was heading more towards semigroups without cancellation where the zero problem explodes
    What for? Division makes less and less sense in that direction. If you’re explaining division (which is the point of this thread) you’re supposed to be heading in the opposite direction, towards division rings and fields – when the cancellation property holds (for nonzero elements).
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  14. #13  
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    Quote Originally Posted by organic god
    rofl jane bennet gets owned by river_rat every maths thread

    The rat got mad mathematical skills
    It's not a competition, dude.
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  15. #14  
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    Quote Originally Posted by JaneBennet
    Quote Originally Posted by river_rat
    I was heading more towards semigroups without cancellation where the zero problem explodes
    What for? Division makes less and less sense in that direction. If you’re explaining division (which is the point of this thread) you’re supposed to be heading in the opposite direction, towards division rings and fields – when the cancellation property holds (for nonzero elements).
    Well for starters my masters is there so I like that area Semigroups are cool, and amazingly important and yet most people never see them until they pump into some serious analysis etc.

    Anyway, going to where division is better and better defined doesn't help you understand it (as you are using it already). You have to go somewhere where it doesn't work the way you are used to to get a grip on its implications.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  16. #15  
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    Quote Originally Posted by river_rat
    Quote Originally Posted by JaneBennet
    Quote Originally Posted by river_rat
    I was heading more towards semigroups without cancellation where the zero problem explodes
    What for? Division makes less and less sense in that direction. If you’re explaining division (which is the point of this thread) you’re supposed to be heading in the opposite direction, towards division rings and fields – when the cancellation property holds (for nonzero elements).
    Well for starters my masters is there so I like that area Semigroups are cool, and amazingly important and yet most people never see them until they pump into some serious analysis etc.

    Anyway, going to where division is better and better defined doesn't help you understand it (as you are using it already). You have to go somewhere where it doesn't work the way you are used to to get a grip on its implications.
    Agreed. You stick with your semigroups, I’ll stick with my fields.
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  17. #16  
    Forum Professor river_rat's Avatar
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    Oh, doing research in field theory?
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  18. #17  
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    Quote Originally Posted by organic god
    rofl jane bennet gets owned by river_rat every maths thread

    The rat got mad mathematical skills
    Totally.
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