From the context I guess colons equals add the implication of setting. As in $t:=0$ means lets set $t=0$.
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What context do you mean? – Henry Lee Jun 30 '19 at 21:39
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1usually the symbol $:=$ means "defined as", and the symbol $=$ is used for equations or say that two statements are the same thing – Masacroso Jun 30 '19 at 21:39
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Sometimes the symbol $:=$ is used in pseudocode of algorithms as the assignment operator – michalis vazaios Jun 30 '19 at 21:41
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1@HenryLee P. 3 in https://shoup.net/ntb/ntb-v2.pdf – ms2r Jun 30 '19 at 21:47
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1Possible duplicate of Difference between $:=$ and $=$ – postmortes Jul 01 '19 at 05:50
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The $t:=0$ notation is borrowed from some computer programming languages. It implies we define $t$ to be $0$, so it's not an equation to be solved e.g. or part of some axiom, but an "assignment" of values.
Henno Brandsma
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The latter is used to define something. For example we have that $2 + 4 = 6$. That is just a normal equality. But if we have something that we want to define then we can use "$:=$". For example we set $A := \lbrace \text{apple},\text{banana} \rbrace$.
Con
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