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Why do some use the equality symbol "$\;\stackrel{\text{def}}{=}\;$" for some definitions? For instance, $$\varepsilon \;\stackrel{\text{def}}{=}\; \frac{\Delta(L)}{L}$$

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  • $\begingroup$ In order to make a distinction with usage of "=" for properties ; example a formula like $S=\frac12$ height $\times$ base does not define area $S$ which has been defined elsewhere. $\endgroup$
    – Jean Marie
    Jun 6 '20 at 8:54
  • $\begingroup$ You will also see definitions given by $:=$ symbol, which finds its origin in computer science languages affectation (even if affectation cannot be reduced to definition), more explicitly, Algol langage (en.wikipedia.org/wiki/Assignment_(computer_science)) $\endgroup$
    – Jean Marie
    Jun 6 '20 at 9:02
  • $\begingroup$ You can also see "$\;\stackrel{\Delta}{=}\;$" for definitions. I prefer "$\;:=\;$", though. Much easier to type. :) $\endgroup$
    – Blue
    Jun 6 '20 at 9:06
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    $\begingroup$ @Blue indeed "$:=$" is better because it make clear what is defined by what, the other symbols are symmetric. By example, I used sometimes the symbol "$=:$" to define the meaning of a symbol after some algebra in the LHS of $=:$ $\endgroup$
    – Masacroso
    Jun 6 '20 at 9:25
  • $\begingroup$ A previous similar question here $\endgroup$
    – Jean Marie
    Jun 6 '20 at 9:43

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