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In the following example, why do these two calls to Apply return different results?

list = {"a", "b"};
Apply[f, list]
Apply[f[#] &, list]

f[a, b]

f[a]

In contrast, when using Map (which is a different function from Apply), these two calls return results identical to each other:

list = {"a", "b"};
Map[f, list]
Map[f[#] &, list]

{f["a"], f["b"]}

{f["a"], f["b"]}

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    $\begingroup$ Keep in mind # is short for Slot[1], which represents (only) the first argument. Also remember Trace or TracePrint: On simple code, such as Apply[f, list] // Trace and Apply[f[#] &, list] // Trace, the Trace gives a nice sequence that shows how an expression is evaluated. (TracePrint shows more and is therefore both more complete and more complicated to follow.) $\endgroup$
    – Michael E2
    Aug 7, 2021 at 18:30
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    $\begingroup$ Another difference, not exhibited in this question, is that if f has Attributes, then f[##] & does not. In practice, this matters most when f has a Hold* attribute such as HoldAll. [A better question might be what are the differences between f and f[#] &.] $\endgroup$
    – Michael E2
    Aug 7, 2021 at 18:41

1 Answer 1

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Oh, I was also surprised by the differenxe, but I have an explanation for it: By using f[#]&, you explicitly say that the functions shall only use the first argument. Use ## otherwise.

Apply[f[#] &, list]
Apply[f[##] &, list]

f["a"]

f["a", "b"]
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