diff --git a/doble b/doble
index d07f80e..3827d3a 100755
Binary files a/doble and b/doble differ
diff --git a/numbers.c b/numbers.c
index 6fcd80c..dbdf078 100644
--- a/numbers.c
+++ b/numbers.c
@@ -11,23 +11,22 @@
   * Duplizieren eines zufälligen Eintrags im Array.
   * in `getDuplicate()`: Sortieren des Arrays und Erkennen der doppelten Zahl durch Vergleich benachbarter Elemente. */
 
-// Comparison function for unsigned integers used in the binary search tree
+// Comparison function for unsigned integers used in BST and sorting operations.
 // Returns: <0 if a < b, 0 if a == b, >0 if a > b
-// This function is passed to addToTree to determine ordering
-int compareUnsignedInts(const void *a, const void *b)
+// This is an internal function (static) since it's not part of the public API.
+static int compareUnsignedInts(const void *a, const void *b)
 {
     unsigned int valA = *(const unsigned int *)a;
     unsigned int valB = *(const unsigned int *)b;
     
-    // Simple subtraction works for unsigned integers in this case
-    // (Note: in general subtraction can overflow, but our range is small)
+    // Safe comparison without overflow concerns for our range
     if (valA < valB) return -1;
     if (valA > valB) return 1;
     return 0;
 }
 
 // Returns len random numbers between 1 and 2x len in random order which are all different, except for two entries.
-// Returns NULL on errors. Use your implementation of the binary search tree to check for possible duplicates while
+// Returns NULL on errors. Use the implementation of the binary search tree to check for possible duplicates while
 // creating random numbers.
 //
 // Algorithm:
@@ -66,7 +65,7 @@ unsigned int *createNumbers(unsigned int len)
         int isDuplicate = 0;
         usedNumbers = addToTree(usedNumbers, &randomNumber, sizeof(unsigned int), compareUnsignedInts, &isDuplicate);
         
-        if (usedNumbers == NULL)
+        if (usedNumbers == NULL) // checks if addTOTree failed 
         {
             free(numbers);
             return NULL;
@@ -103,17 +102,7 @@ unsigned int *createNumbers(unsigned int len)
     return numbers;
 }
 
-// Comparison function for qsort to sort unsigned integers in ascending order
-// Returns: <0 if a < b, 0 if a == b, >0 if a > b
-static int compareUnsigned(const void *a, const void *b)
-{
-    unsigned int valA = *(const unsigned int *)a;
-    unsigned int valB = *(const unsigned int *)b;
-    
-    if (valA < valB) return -1;
-    if (valA > valB) return 1;
-    return 0;
-}
+
 
 // Returns only the only number in numbers which is present twice. Returns zero on errors.
 //
@@ -140,8 +129,8 @@ unsigned int getDuplicate(const unsigned int *numbers, unsigned int len)
     // Step 3: Copy the array
     memcpy(sorted, numbers, len * sizeof(unsigned int));
     
-    // Step 4: Sort the copy
-    qsort(sorted, len, sizeof(unsigned int), compareUnsigned);
+    // Step 4: Sort the copy using the shared comparison function
+    qsort(sorted, len, sizeof(unsigned int), compareUnsignedInts);
     
     // Step 5: Compare adjacent elements to find the duplicate
     for (unsigned int i = 0; i < len - 1; i++)
diff --git a/numbers.o b/numbers.o
index b6079d0..22155d6 100644
Binary files a/numbers.o and b/numbers.o differ
diff --git a/runTest_numbers b/runTest_numbers
index 366d0f2..9d2da0d 100755
Binary files a/runTest_numbers and b/runTest_numbers differ