Is the dealing of hands of cards in the game of Hearts a function?

Aion

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In the game of Hearts, four players are dealt 13 cards from a deck of 52 cards. Is this a function? If so, what sets make up the domain and codomain, and is the function injective, surjective, bijective, or neither?
 
In the game of Hearts, four players are dealt 13 cards from a deck of 52 cards. Is this a function? If so, what sets make up the domain and codomain, and is the function injective, surjective, bijective, or neither?

I don't think there's anything there to call a function ... yet. It's just something someone is doing. But it is a situation within which one might define a function.

The hard part, for me, is to see any sort of input. What ideas do you have?
 
In the game of Hearts, four players are dealt 13 cards from a deck of 52 cards. Is this a function? If so, what sets make up the domain and codomain, and is the function injective, surjective, bijective, or neither?
Let's number the players 1, 2, 3, 4. So if there is a function I would think that 1, 2, 3 and 4 would be the domain. The output would be the 13 cards a player gets, ie f(1) would be the set of 13 cards that player 1 gets. Initially I was going to say that this would not be a function since for one input you get 13 outputs. But here is how you get around that. There are 52C13 different ways of getting dealt 13 cards. If we numbered each possible hand then it seems to be a function. See what you can do with this or tell me why you think it will not work.
 
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Let's number the players 1, 2, 3, 4. So if there is a function I would think that 1, 2, 3 and 4 would be the domain. The output would be the 13 cards a player gets, ie f(1) would be the set of 13 cards that ones get. Initially I was going to say that this would not be a function since for one input you get 13 outputs. But here is how you get around that. There are 52C13 different ways of getting dealt 13 cards. If we numbered each possible hand then it seems to be a fiunction. See what you can do with this or tell me why you think it will not work.

That's one possibility. But you could also take the deck to be the domain, and the function takes each card to a person. That actually seems closer to the nature of what's happening.

This is the trouble with the question: We could define many different functions, depending on what we see as the domain and what mapping we look at.

You could also take an entirely different view, and take the deal to be a function of the results of the shuffle, so that each possible shuffled deck is mapped to a different partition of the cards among the players!
 
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