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Perhaps the natural discomfort many face when confronted by this challenging formulation instead indicates that a limitation of the real number system has been
by berkeleynerd 6y ago
Perhaps the natural discomfort many face when confronted by this challenging formulation instead indicates that a limitation of the real number system has been perceived? I would encourage those who have this reaction to study hyperreal and other alternative systems as mentioned in the article. If this clicks for them they may help lead us in new direction mathematically and advance the state of the art.
- jhanschoo 6y agoThis comes from the fact that most people don't learn limits. Once the definition of the decimal representation is understood to be in terms of a limiting process, the meaning becomes clear. For most purposes hyperreals are too much machinery when learning and manipulating limits would be simpler.