What does "proportional" mean?

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I used to think of $\propto$ as indicating the one quantity is proportional to the other, with possibly an additive constant involved, i.e. $f(x) \propto g(x)$ if $f(x) = ag(x) + b$. Is that reasonable, or does $\propto$ mostly requires $b=0$? Wikipedia seems to refer only to a multiplicative constant.

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1 Answer

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Yes, proportional means related only by a multiplicative constant. When $g(x)$ doubles, so does $f(x)$. If $b \neq 0$ this will not be true.

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