problem updating database

[gilgalbiblewhee]

I don't understand where I'm going wrong in this:

for($j=1; $j<=18; $j++){
    $sql = "UPDATE boti_pages SET chapter = '".$chapTitles[$j][0]."' WHERE page_num >= '".$chapTitles[0][$j]."' AND page_num < '".$chapTitles[0][$j+1]."'";
echo $sql."<br />";
} 

$chapTitles[1][0] = "Introduction"; 
$chapTitles[0][1] =  "1";

$chapTitles[2][0] = "chapter 1";
$chapTitles[0][2] =  "5";

$chapTitles[3][0] = "chapter 2"; 
$chapTitles[0][3] =  "17";

$chapTitles[4][0] = "chapter 3";
$chapTitles[0][4] =  "18";

$chapTitles[5][0] = "chapter 4";
$chapTitles[0][5] =  "27";

$chapTitles[6][0] = "chapter 5";
$chapTitles[0][6] =  "48"; 

Echo-ing the SQL I get:

UPDATE boti_pages SET chapter = 'Introduction' WHERE page_num >= '1' AND page_num < '5'
UPDATE boti_pages SET chapter = 'chapter 1' WHERE page_num >= '5' AND page_num < '17'
UPDATE boti_pages SET chapter = 'chapter 2' WHERE page_num >= '17' AND page_num < '18'
UPDATE boti_pages SET chapter = 'chapter 3' WHERE page_num >= '18' AND page_num < '27'
UPDATE boti_pages SET chapter = 'chapter 4' WHERE page_num >= '27' AND page_num < '48'
UPDATE boti_pages SET chapter = 'chapter 5' WHERE page_num >= '48' AND page_num < '62'

But there is no entry into the database in the chapter field.