Last Updated：2026/01/01
Sentence
This
symbolic
representation
of
ideal
numbers
is
very
convenient,
and
tends
to
abbreviate
many
demonstrations.
Every
ideal
number
is
a
divisor
of
an
actual
number,
and,
indeed,
of
an
infinite
number
of
actual
numbers.
Also,
if
the
ideal
number
𝜙(𝛼)
be
a
divisor
of
the
actual
number
F(𝛼),
the
quotient
𝜙₁(𝛼)=F(𝛼)÷𝜙(𝛼)
is
always
ideal;
for
if
𝜙₁(𝛼)
were
an
actual
number,
𝜙(𝛼),
which
is
the
quotient
of
F(𝛼)
divided
by
𝜙₁(𝛼),
ought
also
to
be
an
actual
number.
Quizzes for review
This symbolic representation of ideal numbers is very convenient, and tends to abbreviate many demonstrations. Every ideal number is a divisor of an actual number, and, indeed, of an infinite number of actual numbers. Also, if the ideal number 𝜙(𝛼) be a divisor of the actual number F(𝛼), the quotient 𝜙₁(𝛼)=F(𝛼)÷𝜙(𝛼) is always ideal; for if 𝜙₁(𝛼) were an actual number, 𝜙(𝛼), which is the quotient of F(𝛼) divided by 𝜙₁(𝛼), ought also to be an actual number.
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