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Uhhhh...no. Take a look at Dedekind cuts.

• schoen 10y ago
  The linked video is largely a critique of Dedekind cuts, arguing that they don't in general let us recognize, distinguish, or perform arithmetic on most real numbers. (Almost all of the informational input to a Dedekind cut for a randomly chosen real couldn't be written, remembered, or specified in any way by a human being.) I think the presenter in the video is trying to justify a kind of finitist attitude based on the inaccessibility and unspecifiability of reals-in-general to us. This could also be advocating a position something like https://en.wikipedia.org/wiki/Computable_number#Can_computable_numbers_be_used_instead_of_the_reals.3F https://en.wikipedia.org/wiki/Computable_number#Can_computab... Edit: or perhaps https://en.wikipedia.org/wiki/Constructive_analysis https://en.wikipedia.org/wiki/Constructive_analysis (I didn't watch enough to understand exactly what alternative he proposes)
  • jackmaney 10y ago
    > Almost all of the informational input to a Dedekind cut for a randomly chosen real couldn't be written, remembered, or specified in any way by a human being. Well, yes. The reals are uncountable.