Mathematically Precise Definition of Unit

[marschmellow]

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?

 

[pwsnafu]

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 "l_m" and inch would be "l_i" and define l_i = 0.0254 l_m.

Edit: I hate the fact they spell it "meter" in the US. :grumpy:

 

[Stephen Tashi]

"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.