Last Updated：2025/12/20
Sentence
There
have
been
several
classical
constructions
of
the
reals
that
avoid
these
problems,
the
most
famous
ones
being
Dedekind
Cuts
and
Cauchy
Sequences,
named
respectively
for
the
mathematicians
Richard
Dedekind
(1831
-
1916)
and
Augustine
Cauchy
(1789
-
1857).
We
will
not
discuss
these
constructions
here,
but
will
use
a
more
modern
one
developed
by
Gabriel
Stolzenberg,
based
on
"interval
arithmetic."
Quizzes for review
There have been several classical constructions of the reals that avoid these problems, the most famous ones being Dedekind Cuts and Cauchy Sequences, named respectively for the mathematicians Richard Dedekind (1831 - 1916) and Augustine Cauchy (1789 - 1857). We will not discuss these constructions here, but will use a more modern one developed by Gabriel Stolzenberg, based on interval arithmetic.
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