Solve another one

1 files changed, 13 insertions, 0 deletions

diff --git a/0x01/README.md b/0x01/README.md
index c0daa8a..38bed54 100644
--- a/0x01/README.md
+++ b/0x01/README.md
@@ -295,6 +295,19 @@ properties.
 
   e. If `k < d`, then `p(n) = w(n^k)`.
 
+    To provie this we need the little-omega formula which says:
+    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`
+
+    We can try to fit the function into this formula.
+    `0 <= c * g(n) < f(n)`
+    `0 <= c * (ak * n^k) < f(n)`.
+    Since `k` is less than `d` we can also say
+    `0 <= c * (ak * n^k) < c * (ad * n^d) < f(n)`.
+    This is enough to satisfy the constraints of the formula so that we can
+    claim that `p(n) = w(n^k)` because any constant c greater than 0 will work.
+
 1. Exercise 4.1-2 from the textbook (10 marks)
 
   What does `FIND-MAXIMUM-SUBARRAY` return when all elements of `A` are negative?