Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
aa:lab:05 [2020/11/09 10:08] pdmatei |
aa:lab:05 [2020/11/15 13:11] (current) fabianpatras |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ====== Lab 05 - Asymptotic notations ====== | + | ====== Lab 06 - Asymptotic notations ====== |
| Line 12: | Line 12: | ||
| ==== 2. Properties of asymptotic notations ==== | ==== 2. Properties of asymptotic notations ==== | ||
| - | **2.1** Prove that if $math[lim] $math[g(n) \over f(n)] $math[= 0] implies that $math[g(n) \in o(f(n))], for n reaching infinity. Hint: use the "epsilon" or "Cauchy" limit definition for sequences. | + | **2.1** Prove that if $math[lim_{n\rightarrow \infty}] $math[g(n) \over f(n)] $math[= 0] implies that $math[g(n) \in o(f(n))], for n reaching infinity. Hint: use the "epsilon" or "Cauchy" limit definition for sequences. |
| **2.2** Prove that $math[f(n) \in Ω(log(n))] and $math[g(n) \in O(n)] implies $math[f(n) \in Ω(log(g(n)))]. | **2.2** Prove that $math[f(n) \in Ω(log(n))] and $math[g(n) \in O(n)] implies $math[f(n) \in Ω(log(g(n)))]. | ||