EDB β€” 1FB

↑ ← β†’ ↓ view in whole PDF view in whole HTML

View

English

Definition 35

[1FB]Let aβˆˆβ„β€• and I be a neighborhood of a. Let f,g:I→ℝ. We will say that ”f(x)=o(g(x)) for x tending to a” if 1

βˆ€Ξ΅>0, βˆƒΞ΄>0,x∈I∧ |xβˆ’a|<Ξ΄β‡’|f(x)|≀Ρ|g(x)|.

This notation reads like ”f is small o of g”.

If g(x)≠0 for x≠a, then equivalently we can write

limx→af(x)g(x)=0.

We will say that ”f(x)=O(g(x)) for x tending to a” if if there is a constant c>0 and a neighborhood J of a for which βˆ€x∈J,|f(x)|≀c|g(x)|.

Again, if g(x)≠0 for x≠a, then equivalently we can write

lim supxβ†’a|f(x)||g(x)|<∞,

This notation reads like ”f is big O of g”.

For further information, and more notations, see [ 45 ] .

This notation is usually attributed to Landau.

  1. Consider that J={x∈I: |xβˆ’a|<Ξ΄} is a neighborhood of a.
Download PDF
Bibliography
Book index
  • Taylor's theorem
  • small o , see Landau symbols
  • big O , see Landau symbols
  • Landau symbols
Managing blob in: Multiple languages
This content is available in: Italian English