Notation of an element of a tuple

Question

Suppose $F$ a set of $n$ fruit baskets

$$F = \{f_1, f_2, ..., f_n\}$$

The baskets can contain up to 3 types of fruits where:

• $P$: Number of peaches
• $B$: Number of bananas
• $A$: Number of apples

Each basket contains a different number of fruits and can be represented as a tuple: $$f_n = (P, B, A)$$

My question is: If I want to get the number of Apples in the basket $f_2$ or if I want to get the number of Peaches in the basket $f_3$: Can I represent them as $A(f_2)$ and $P(f_3)$ respectively? Or how is the correct way to get specific elements of tuples with that letters?

Answer 1

You can introduce any mathematical notation that you want, as long as use define it precisely (and as long as it does not fly in the face of well-established notation). In your case, I would write

In the following, I will let $A(f_n)$ denote the number of apples in basket $f$. Similarly, $P(f_n)$ and $B(f_n)$ denote the number of peaches and bananas, respectively.