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Mathematically Precise Definition of Unit

  1. Feb 20, 2012 #1
    Does anyone know exactly what kind of mathematical object a unit (like meters, coulombs, etc.) is? Or what kind of algebraic structure units are elements of?
  2. jcsd
  3. Feb 20, 2012 #2


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    Units of measurement is not a mathematical quantity. We use them to calibrate our experiments. I guess you could try to create a structure for them.

    "2 candlesticks" times "3 cabdrivers" = 6 [candlestick][cabdriver].

    That has the same structure as

    (2x) (3y) = 6xy,

    and we can add and subtract if the units are the same: 3 cadlesticks + 2 candlesticks = 5 candlesticks is the same thing 3x+2x = 5x.

    So polynomials. You could let "l" be length and then metre would be "lm" and inch would be "li" and define li = 0.0254 lm.

    Edit: I hate the fact they spell it "meter" in the US. :grumpy:
    Last edited: Feb 20, 2012
  4. Feb 20, 2012 #3

    Stephen Tashi

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    "Dimensional Analysis" is a branch of applied mathematics (or is it properly called physics?). It is based on the idea that the units in equations that describe physical laws must work out properly, but I don't know if it gives a formal definition of such units.
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