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OK I edited the question. Sorry for the wrong terms.

What is the correct notation such that a specific function maps an element of a specific sequence/list/n-tuple to its index?

I have researched about index sets but it only gives index to a set and not to the element.

Is there a way to draw the notation of the index of the element like in the index sets?

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    Sets don't have order; $\{1,2\}$ is the same thing as $\{2,1\}$, so there is no such thing as "its index in the set". If you have an ordered tuple, there is no specific notation for it.2012-04-26

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