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 $t \triangleq m$ (generally) means: "$t$ is defined to be $m$" or "$t$ is equal by definition to $m$" (often under certain conditions).
In a similar sense, some use $:=$ or $=:$ (see for instance Symbols based on equality). Yet, this Delta variant is more important to me.
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 letter "D", i.e. for the initial of "definition". Indeed, one sometimes finds $\overset{\mathrm{def}}{=}$ too. In German apparently, one also uses $≙$ (Entspricht-Zeichen, with Unicode U+2259).
Based on these prior hints, my questions are as follows:
- Who introduced this dual symbol first in science, and where (which source)?
- What motivated the Greek $\Delta$ notation? The abbreviation of some word, a symbol (why not a latin notation)?
- 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:
- SE.math: What is meant by the delta equivalent sign?
- SE.tex: Delta-equal to symbol