Both array_push and the method you described will work.
$cart = array();
$cart[] = 13;
$cart[] = 14;
// etc
//Above is correct. but below one is for further understanding
$cart = array();
for($i=0;$i<=5;$i++){
$cart[] = $i;
}
echo "";
print_r($cart);
echo "
";
Is the same as: