Number Divided By Zero

Discussion in 'Algebra' started by nycmathguy, Jul 20, 2021.

  1. nycmathguy

    nycmathguy

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    Let n = any number

    Why is n/0 undefined?

    I know that it is impossible to divide something from nothing.

    Explain.
     
    nycmathguy, Jul 20, 2021
    #1
  2. nycmathguy

    MathLover1

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    In general, a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.
     
    MathLover1, Jul 21, 2021
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  3. nycmathguy

    nycmathguy

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    Do you think some genius will discover in the future that division by 0 is possible?
     
    nycmathguy, Jul 21, 2021
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  4. nycmathguy

    MathLover1

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    might be possible
     
    MathLover1, Jul 22, 2021
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  5. nycmathguy

    nycmathguy

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    You are right.

    You forgot to reply to Questions Part 4 in your inbox here. I also want to change the way you and I go through the precalculus textbooks. Expect a new PM in just a few minutes.
     
    nycmathguy, Jul 22, 2021
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  6. nycmathguy

    conway

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    I am not a genius. Yet I have provided a solution for division by zero. See the thread "The Unified Number". I was able to do so because I am a philosopher not a mathematician. The "theory" begins with philosophical axioms.

    Numerus Numerans = absract numbers
    Numerus Numeratus = concrete numbers

    Numbers are defined as "numerical quantities". Yet if we add to that definition "dimensional quantities" or "units" in regards to absract numbers (concrete numbers already have "units"). We can have...

    Numerus "Numerans Numeratus" = The Unified Number
     
    conway, Feb 19, 2024
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  7. nycmathguy

    HallsofIvy

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    If n/m= a then n= am
    If n/0= a then n= a*0= 0

    So if n is not 0 n/0 is not ANY number.
    We say that n/0, for n non-zero, is "undefined".

    0/0 is a little different.
    If 0/0= a then 0= a*0
    But that is true every a.
    We say that 0/0 is "undetermined".
     
    HallsofIvy, Feb 25, 2024
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  8. nycmathguy

    conway

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    a=/=0

    If I have (a) of anything, number or otherwise.

    I multiple (a) by (0)...

    a*0 = 0

    Why does (a) disappear?

    The multiplicative identity property of zero?

    Properties are changed all the time in mathematics....see "wheels" and "meadows"....

    So why not this property....I have NEVER seen anything disappear. I might not know where it went. Or have seen it leave. But it did not disappear.
     
    conway, Feb 26, 2024
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  9. nycmathguy

    HallsofIvy

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    The "distributive law": For any numbers, a, b, and c, a(b+ c)= ab+ ac.
    Since "0" is the additive identity, x+ 0= x.
    Taking c=0, ab= a(b+ 0)= ab+ a(0)
    Subtracting ab from both sides 0= a(0).
     
    HallsofIvy, Feb 26, 2024
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  10. nycmathguy

    conway

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    I have shown specifically (with definitions), how the additive identity can be kept. As well as the distributive field axiom. I have shown how all field axioms remain unchanged. It is only a matter of changing the "properties" of numbers. Allow all numbers to be composed of numerical quantities, and dimensional unit quantities. You have but to give me the chance. For example...see the section "Distributive" in the thread "The Unified Number".

    I would copy and paste, but "notation" is lost in translation. "Copy and paste" will not translate "underscores". Which is essential notation for the concept.

    I appreciate your time, and intelligence. Especially knowing that I exasperate you.
     
    Last edited: Feb 27, 2024
    conway, Feb 27, 2024
    #10
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