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

Blue
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Jules_fr
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  • 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. – Jean Marie Jun 06 '20 at 08:54
  • 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 (https://en.wikipedia.org/wiki/Assignment_(computer_science)) – Jean Marie Jun 06 '20 at 09:02
  • You can also see "$;\stackrel{\Delta}{=};$" for definitions. I prefer "$;:=;$", though. Much easier to type. :) – Blue Jun 06 '20 at 09:06
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    @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 $=:$ – Masacroso Jun 06 '20 at 09:25
  • A previous similar question here – Jean Marie Jun 06 '20 at 09:43
  • Merci beaucoup Jean Marie! – Jules_fr Jun 06 '20 at 13:30
  • @Masacroso I always hated that symbol. It’s too phallic for my taste (which is saying a lot considering that’s my preferred sex, lol) – gen-ℤ ready to perish Jun 06 '20 at 15:19
  • I type equivalent sign in the search box, and I did not see the Distinguishing definitions from equivalences. – Xander Henderson 1 – Jules_fr Jun 06 '20 at 15:48

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