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I'm not pretty sure about how good I understood the explanation our teacher provide when we delve in fundamentals of set theory:

(1) A uniquely identifies B, which subsequently means that any unique tuple A has could be used in searching for an associated member/tuple/item of B.

Moreover, the "mathematical" expression could be laid down as follows:

$ A \rightarrow B $

s.t. for every tuple t1, t2 which belong to the relational schema r we could say: t1[A] != t2[A] => t1[B] = t2[B]

The question: What does $A \rightarrow B$ in set theory and database represent? (1)

Thank you in advance and for any incoherence or inaccuracy in text don't retain yourself from rising/flagging the inconveniences.

Mauro ALLEGRANZA
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Paradoxac
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  • Hello! The formatting of this post looks a bit unfortunate. Did you know that putting asterisk makes italic, and two asterisks a bold font? – Aig Mar 10 '24 at 12:16
  • ops... No, I haven't. Let me settle this issue. – Paradoxac Mar 10 '24 at 13:27
  • You probably will be better looking at where they discuss relational calculus https://math.stackexchange.com/questions/3791399/suggested-resources-for-self-teaching-relational-algebra-calculus – jimjim Mar 10 '24 at 13:59
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    For $A \to B$, this means "function", i,e, "A maps to B": "for each element (tuple?) of $A$ "there is an associated member (tuple) of B". – Mauro ALLEGRANZA Mar 11 '24 at 08:55
  • Hello. I worked out the answer and I'm about to answer my own question in a coherent and eloquent way just to clarify any confusion my poor way of framing the question might have stirred up amongst you. – Paradoxac Mar 15 '24 at 20:52

1 Answers1

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The "$\to$" symbol has many meanings in mathematics, depending on the context.

Without further details, I would read "t1[A] != t2[A] => t1[B] = t2[B]" simply as:

"if t1[A] ≠ t2[A], then t1[B] = t2[B]"

Regarding $A → B$ [also $A ↦ B$], this means function, i,e, "A maps to B".

In the context above: "for each element (tuple?) of A there is an associated member (tuple) of B".

Mauro ALLEGRANZA
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