Analysis with computable numbers

Is it possible to define a different type of analysis that only uses the computable numbers? Would limits, continuity, derivatives, etc still make sense? Would any important results not work out? It never sat well with me that every number we’ve basically ever worked with is computable but almost every real number is uncomputable. This way you’d be able to avoid uncountable sets which to me would seem much simpler.

submitted by /u/Richard_Fey
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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs

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