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0 pointsmoyix12y ago0 comments

One possible replacement is the computable numbers [1]; this includes the algebraic numbers and some common transcendentals (e, pi), and you can even build up something akin to standard analysis (computable analysis [2]).

[1] http://en.wikipedia.org/wiki/Computable_number

[2] http://en.wikipedia.org/wiki/Computable_analysis

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gizmo68612y ago

Unfourtuantly, there exist numbers which are definable but not computable.

moyixOP12y ago

Sure. Chaitin's Omega is a good example. The question is whether such numbers occur in the real world.

jfarmer12y ago

The trick here is defining "occur" and "real world" precisely. Are you saying the act of me writing down those symbols and expressing the idea does not count as "occurring in the real world?" ;)

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