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One symbol used for defining objects is "$\overset{def}{=}$". Let's say we introduce a new symbol $B$ which should be defined as $A$. Is $\overset{def}{=}$ then used as

$$ A\overset{def}{=}B $$ or $$ B\overset{def}{=}A $$

or is this just a subjective question?

HerpDerpington
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    This is a subjective question, but I'd usually use the latter. Actually, I'd probably write $B := A$, which is unambiguous and can be reversed to $A =: B$ if the situation called for it, for some reason (perhaps a diagram?). – jpmacmanus Apr 20 '23 at 12:03
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    Yeah, the : on the symbol := has the good effect of desymmetrizing the relation. Still, though, I prefer words in this situation, as much as is possible anyway: "Let $A$ be defined as $B$" – Lee Mosher Apr 20 '23 at 12:07
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    Usually, I'd say the side that is typographically and visually significantly simpler is the one being defined, and the side that is typographically more complex is the side that contains the definition. I'm sure there are exceptions to this, but visual simplicity is an important reason to make such definitions in the first place. And when it isn't the reason, it is often still a secondary goal. – Arthur Apr 20 '23 at 12:09
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    Equality, like "logical equivalence" is bi-directional: it states that we can replace one expression with the other one. The "usual reading" (at least in countries that writes from left to right, I suppose) is : definiendum = definiens. – Mauro ALLEGRANZA Apr 20 '23 at 12:21
  • See e.g. W&R, Principia Mathematica (1910), page 11. – Mauro ALLEGRANZA Apr 20 '23 at 12:28

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