Note 73 — Chapter II · THE MEANING OF NUMBERS
Charles Francis Atkinson translation
The technical difference (in German usage) between Grenz and Grenzwert is in most cases ignored in this translation as it is only the underlying conception of “number” common to both that concerns us. Grenz is the “limit” strictly speaking, i.e., the number a to which the terms a1₁, a2₂, a₃ ... of a particular series approximate more and more closely, till nearer to a than any assignable number whatever. The Grenzwert of a function, on the other hand, is the “limit” of the value which the function takes for a given value a of the variable x. These methods of reasoning and their derivatives enable solutions to be obtained for series such as (1⁄m¹,) (1⁄m²,) (1⁄m³,) ... (1⁄mx) or functions such as
x(2x - 1)
y = —————
(x + 2)(x - 3)
where x is infinite or indefinite.—Tr.