work on assignment 1

1 files changed, 31 insertions, 5 deletions

diff --git a/notes.md b/notes.md
index 4cd2d1b..de455b5 100644
--- a/notes.md
+++ b/notes.md
@@ -942,12 +942,19 @@ Example:
 
 instead of guessing the value you can make it as 2n+3
 
+Little-oh
+---------
+
+The function `f(n) = o(g(n))` for any positive constant `c > 0`,
+if there exists a constant `n0 > 0` such that `0 < f(n) < c * g(n)`
+for all `n >= n0`.
+
 
 Omega
 ----
 
-The function `f(n) = omega(g(n)) if positive contstants c and n0`
-such that `f(n) >= c * g(n) V n>=n0`
+The function `f(n) = omega(g(n))` if there exists positive contstants c and n0
+such that `0 <= c * g(n) <= f(n)` for all `n >= n0`.
 
 e.g.
 
@@ -963,13 +970,32 @@ f(n)     c * g(n)
  true f(n) = omega(logn)
 ```
 
+little-omega w-notation
+----------
+Denotes a lower bound that is not asymptotically tight.
+
+The function `f(n) = w(g(n))` for any positive constant `c > 0`,
+if there exists a constant `n0 > 0`
+such that `0 <= c * g(n) < f(n)` for all `n >= n0`
+
+the relation `f(n) = w(g(n))` implies that:
+
+```plaintext
+lim         f(n)
+            ---- = infinity
+n->infinity g(n)
+```
+if the limit exists. That is `f(n)` becomes arbitrarily large relative to `g(n)`
+as `n` approaches infinity.
+
+
 Theta
 -----
 
-The funciton `f(n)=theta(g(n)) if 3 +ve constants c1,c2 and n0`
-such that `c1*g(n) <= f(n) <= c2*g(n)`
+The function `f(n)=theta(g(n))` if there exists positive constants c1, c2, and n0
+such that `0 <= c1 * g(n) <= f(n) <= c2 * g(n)` for all `n >= n0`. (n0 is pronounced enn-not)
 
-f(n) = theta(n)
+f(n) = theta(g(n))
 
 ```
 eg.