Definition:Asymptotic Equality/Sequences/Definition 1

Definition

Let $\sequence {a_n}$ and $\sequence {b_n}$ be sequences in $\R$.

Let $b_n \ne 0$ for all $n$.

$\sequence {a_n}$ is asymptotically equal to $\sequence {b_n}$ if and only if:

$\ds \lim_{n \mathop \to \infty} \dfrac {a_n} {b_n} = 1$

Also see

• Equivalence of Definitions of Asymptotically Equal Sequences

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 17.1$
• 1979: G.H. Hardy and E.M. Wright: An Introduction to the Theory of Numbers (5th ed.) ... (previous) ... (next): $\text I$: The Series of Primes: $1.6$ Some notations