Hopefully someone better educated than me can answer this - several of the definitions in the link feel constructivist, i.e. they describe constructions of of real numbers. It seems easy to think of methods of constructing non-rational numbers, by e.g. using infinite sequences, by taking roots, or whatever.
It seems harder to prove that every real number can be constructed via such a method.
Is there a construction-based method that can produce ALL real numbers between, say, 0 and 1? This seems unlikely to me, since the method of construction would probably be based on some sort of enumeration, meaning that you would only end up with countably many numbers. But maybe someone else can help me become un-confused.
thatguysaguy · 59m ago
Joel's blog in general is an extremely great read. I highly recommend subscribing.
morpheos137 · 16m ago
Real numbers are the concept of quantities built up from continuous flows.
moc_was_wronged · 2m ago
Something we made up before we knew Avogadro’s Number and no longer need.
It seems harder to prove that every real number can be constructed via such a method.
Is there a construction-based method that can produce ALL real numbers between, say, 0 and 1? This seems unlikely to me, since the method of construction would probably be based on some sort of enumeration, meaning that you would only end up with countably many numbers. But maybe someone else can help me become un-confused.
(That was trolling.)