Last Updated：2022/12/24
We could say that a Gaussian integer is larger than another if its norm is larger, that is, if its distance from the origin is larger. That's all right, although it has the peculiarity that 5 is larger than -7 as an integer, but smaller than -7 as a Gaussian integer! In a way, this notion of larger makes more sense: shouldn't -7 be considered larger than 5?
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We
could
say
that
a
Gaussian
integer
is
larger
than
another
if
its
norm
is
larger,
that
is,
if
its
distance
from
the
origin
is
larger.
That's
all
right,
although
it
has
the
peculiarity
that
5
is
larger
than
-7
as
an
integer,
but
smaller
than
-7
as
a
Gaussian
integer!
In
a
way,
this
notion
of
larger
makes
more
sense:
shouldn't
-7
be
considered
larger
than
5?
