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$\left [ \left \{ 1,2,3,4 \right \}! \right]^{-1}$Is this the correct notation if one wanted to obtain the factorial for each number in a sequence and then take the sequence and inverse each number in it?

Kaz
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  • What's the $\mathbb{N}$ for? In mathematics it isn't customary to apply operations pointwise to a sequence like that. (Instead we apply operations pointwise to a function.) – Qiaochu Yuan May 07 '13 at 03:18
  • Ah, I'm learning sequences and I still have to get the notation down, thanks! And I need to edit that N out. – Kaz May 07 '13 at 03:23
  • Reminds me of APL, a very clever (too clever) very compact (too compact) programming language. In principle if is OK, if $f$ is a function and $A$ is a subset of the domain, then $f(A)$ has a clear meaning. But not a good idea. – André Nicolas May 07 '13 at 03:26
  • You might find this interesting: Wikipedia :: Map (higher-order function) – kahen May 07 '13 at 03:29
  • Wow thanks! It is not customary to apply operations to sequences, as Qiaochu said. Is there anyway to write it so it is correct? – Kaz May 07 '13 at 03:32

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I would just write $a_n=\frac 1{n!}$, or if the sequence were defined somewhere else as $b_n$, say $c_n=\frac 1{b_n!}$

Ross Millikan
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