math 117 ucsb
| Front | State the limit theorem for scalar multiplication (Theorem 9.3) |
| Back | If lim sₙ = s and k ∈ ℝ, then lim(ksₙ) = k·lim sₙ = ks. |
| Front | Define lim sup and lim inf (Definition 10.5) |
| Back | Let uₙ = inf{sₖ : k > N}, vₙ = sup{sₖ : k > N}. Then lim inf sₙ = lim uₙ and lim sup sₙ = lim vₙ. |
| Front | Define monotone sequences (Definition 10.1) |
| Back | (sₙ) is increasing if sₙ ≤ sₙ₊₁ for all n. (sₙ) is decreasing if sₙ ≥ sₙ₊₁ for all n. Both are called monotone. |