I think it’s just inherent in the math. Dimensions or units are just part of the math, part of the language we use to conceptualize the universe. https://terrytao.wordpress.com/2012/12/29/a-mathematical-formalisation-of-dimensional-analysis/

]]>In thermodynamics exist equations with the form:

dx/x = c/y^2 dy

Where c, x and y are dimentionful quantities. By taking indefinite integrals one gets

log x = – c / y + constant

If log x is an element of an one dimensional affine space (as said above), what exactly (or exactly enough for a non mathematician ;-) ) means the equality? Where does “constant” belong? and – c / y ? There are dimensional inconsistencies? If x units are Kelvin, what is the log x unity?

Thanks.

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