ideal number

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.