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Re: Mathematical Formulas In Programming

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Brian writes:

> Hi, somebody told me that mathematical formulas can be used in
> programming to represent a list of certain words that you want, but
> that you have to tell the program to convert the formulas to the
> exact list of words.  Is it even possible to do that?

You should have asked that someone to explain what they meant. In
particular, what counts as a mathematical formula.

Why wouldn't ['three', 'little', 'mice'] appearing in a program source
code be a mathematical formula representing the list of the three
words 'three', 'little', and 'mice'? But accepting it as a formula
makes the question trivial.

Regular expressions can be, and are, used to specify certain
interesting sets of strings in programming, including large
vocabularies of human languages. Such expressions can also specify
processes like compounding that make the sets technically infinite, so
a finite representation cannot be a simple list. Regular expressions
come with a large number of useful mathematical operations if you
accept union, intersection, complement, and difference of sets,
concatenation and repetition of strings, and so on, as mathematical,
and they come with a practical implementation in terms of finite
automata. It's not trivial but it's done in practice.

Goedel coding could in principle be used to represent any finite list
of words as a number. This is not done in practical programming. I
suppose it belongs in something like mathematical logic as a technique
of proving what can or cannot in principle be done at all.

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Thread

Mathematical Formulas In Programming Brian <briansipler@yahoo.com> - 2012-12-28 13:17 -0800
  Re: Mathematical Formulas In Programming Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2012-12-29 11:58 +0200
    Re: Mathematical Formulas In Programming Brian <briansipler@yahoo.com> - 2012-12-29 04:54 -0800
  Re: Mathematical Formulas In Programming Rui Maciel <rui.maciel@gmail.com> - 2012-12-29 13:26 +0000
    Re: Mathematical Formulas In Programming Brian <briansipler@yahoo.com> - 2012-12-29 07:55 -0800
      Re: Mathematical Formulas In Programming Roberto Waltman <usenet@rwaltman.com> - 2013-01-06 16:54 -0500

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