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Question Number 211791 by mathkun last updated on 20/Sep/24

$$\mathrm{can}\mathrm{someone}\mathrm{please}\mathrm{tell}\mathrm{me}\mathrm{the}\mathrm{difference}\mathrm{b}/\mathrm{w}(=)\mathrm{and}(::=)$$$$$$$$\mathrm{I}\mathrm{searched}\mathrm{up}\mathrm{and}\mathrm{showed}\mathrm{it}\mathrm{was}\mathrm{related}\mathrm{to}\mathrm{assertion},\mathrm{definition},\mathrm{propert}\mathrm{def}....\mathrm{i}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know}.\mathrm{please}\mathrm{help}$$

Answered by Frix last updated on 20/Sep/24

$$a=ba\mathrm{is}\mathrm{equal}\mathrm{to}b$$$$a:=ba\mathrm{is}\mathrm{defined}\mathrm{as}b$$$$$$$$\mathrm{Example}:$$$$x\in \mathbb{C}:\mathrm{sign}\left(x\right)=\frac{x}{\mid x\mid }$$$$\Rightarrow \mathrm{sign}\left(0\right)\mathrm{is}\mathrm{not}\mathrm{naturally}\mathrm{defined}$$$$\mathrm{Sometimes}\mathrm{we}\mathrm{might}\mathrm{need}\mathrm{sign}\left(0\right)=0\mathrm{and}$$$$\mathrm{in}\mathrm{this}\mathrm{case}\mathrm{we}\mathrm{define}\mathrm{sign}\left(0\right)=0\mathrm{which}\mathrm{is}$$$$\mathrm{written}\mathrm{as}\mathrm{sign}\left(0\right):=0$$$$\mathrm{Sometimes}\mathrm{sign}\left(0\right):=1\mathrm{might}\mathrm{work}\mathrm{better}.$$

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