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sequence

Defines: 
generalized sequence, transfinite sequence, finite sequence
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

03E10 no label found40-00 no label found

Comments

From one high school book from 1964, revisited by Slovene mathematician Ivan Vidav and written by Alojzij Vadnal goes this simple definition for sequence:

Sequence is any number set, which is arranged in a way that one number comes first, one second, one third and it is possible for every number of the set to define at which place of the sequence it stands.

Question is: function and number set can not be the same thing? Instead of functional notation f(0), f(1), f(2), ... we use {x_0, x_1, x_2, ... } what in the other side shows a structure of a set.
Am I missing some here? Once I have done one similar "ambiguity" when I said: if we *do this and that*, then we get a set of integer sequences. I should simply say: then we get integer (integral) sequences, because sequences are already sets. Best regard.

I'm just wondering: has anyone here studied the Hofstadter sequences? (Such as the Q sequence: 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 8, 10, 9, 10, 11, 11, 12, 12, 12, 12, 16, 14, 14, ...

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