# Who first defined the “equal-delta” or “delta over equal” ($\triangleq$) symbol?

The symbol $$\triangleq$$ is sometimes used in mathematics (and physics) for a definition. It is instantiated for instance in the Unicode Character 'DELTA EQUAL TO' (U+225C). The notation $$t \triangleq m$$ (often) means: "$$t$$ is defined to be $$m$$" or "$$t$$ is equal by definition to $$m$$" (often under certain conditions). In a similar sense, some uses $$:=$$ or $$=:$$ (see for instance Symbols based on equality). The SE. Maths post What is meant by the delta equivalent sign? proposes a slight distinction (not crystal-clear to me) between the above similar senses:

Sometimes it is used with the slightly different meaning of "equal by definition", to underline the difference w.r.t. "$$:=$$ " which is the definition itself. i.e.

$$a:=3;\\ 5+a \triangleq 5 + 3 = 8$$

I always took for granted that the $$\Delta$$ stood for "D", i.e. for the initial of "definition". Indeed, one sometimes finds: $$\overset{\mathrm{def}}{=}$$ too. Now I am in doubt.

• Who introduced this dual symbol first, and where?
• What motivated the Greek $$\Delta$$ notation? The abbreviation of some word, a symbol?
• Why not merge the lower bar of the Delta with the upper bar of the equal sign, to save some ink, and create a lighter symbol?

References: the symbol itself was already discussed in StackExchange:

• This notation seems very strange, as it suggests symmetry between the definiens and the definiendum. I am more used to := or =:, with the colon on the side of the definiendum. – Margaret Friedland Sep 5 '16 at 1:45
• Mathsym jeff560.tripod.com/mathsym.html has only $=_{\mathrm{Def}}$ (from 1894) but not the Delta version. – Gerald Edgar Sep 5 '16 at 13:44
• @MargaretFriedland The asymmetry is given by what is before the symbol and what is after the symbol. Thus $A \triangleq B$ always means "A is defined to be B". – juanrga Mar 19 '18 at 19:42
• @MargaretFriedland, I am sympathetic to your objection, and, in fact, would go so far as to object somewhat to the $:=$ usage, since it lends itself to typos so easily. Rather, I'd strongly prefer that the context clarify any asymmetry (such as a definition or notational abbreviation) in a mathematical equality. (Mathematicians seem unlikely to take these asymmetries as seriously as programmers may, so I don't necessarily trust them!) – paul garrett Jun 28 '18 at 23:43