Check for positive integers in Javascript: performance and security

I have written (and copied) a few lines of Javascript and it serves my purpose well. But I am trying to figure out a better way (cross-browser and better performance) of doing this. I copied the isInteger function from a friend but I do not understand why we are checking against a string value in the following condition:

if (((c < "0") || (c > "9"))) return false;

The above condition works fine but when I change it to check against number values, the functionality breaks. The input field starts accepting alphabetical characters. Here is how it looks when I change it:

if ((( c < 0 ) || ( c > 9 ) return false;

I have tried to comment out sections so that you can understand what's happening. Also are there any security holes in this code? I read that the 1innerHTML1 method can open some security holes and hence we need to perform a 'clean' operation with it. Hence I chose to use jQuery's .html method (I am new to JavaScript)

The page in question: http://thehotdeal.net/clients/wehtmlit/index.php?order/

$(document).ready(function() {
  var total = 0;
  function calcTotal() {
  /* fetching some values from PHP variables and then performing calculations.
    essentially this is multiplying number of pages by price per page
  */
  /* <![CDATA[ */
    var total_price_main_pages = ($("#pages").attr("value")) * (<?php echo $main_price; ?>),
    total_price_sub_pages = ($("#subpages").attr("value")) * (<?php echo $sub_price; ?>);
    /*  ]] > */
    $("input.calculate:checked").each(function() {
    // This happens for each checked input field
    // These are few additional otions available to the user. If selected then
    // the price stored in their "data" attribute is added to the total
      var value = $(this).attr("data");
      total += parseInt(value); 
    });
    total += (parseInt(total_price_main_pages)) + (parseInt(total_price_sub_pages));
    $("#total").html("Total: <strong>" + total + "</strong>");
  }
  // This happens when the page loads
  calcTotal();
  $("input.calculate").click(function() {
    total = 0;
    calcTotal();
  });
  // function to check if an input is positive number(s). returns true if [ 0 <= s <= 9 ]
  function isInteger(s) {
    var i;
    for (i = 0; i < s.length; i++) {
      var c = s.charAt(i);
      if (((c < "0") || (c > "9"))) return false;
    }
    return true;
  }
  // Checking the mainpage input (default value 1)
  // (valid value is greater than or equal to 1 and less than 10)
  $("#pages").keyup(function() {
    var page = $(this).val();
    // if user deletes the value in this input (blank)
    // then just display a warning message and do nothing
    if(page == ""){
      this.value = "";
      $("#pageError").html("Please enter a value equal or greater than 1.");
      return false;
    }
    // if value is less than or equal to zero then
    // then set 1 as the new value, remove the error message and call the calcTotal function
    else if(page <= 0){
      this.value =1;
      $("#pageError").empty();
      total = 0;
      calcTotal();
    }
    // check if value is not a positive integer by calling the isInteger function
    // if not a positive integer then set 1 as the new value,
    //remove the error message and call the calcTotal function
    else if(!isInteger(page)){
      this.value =1;
      $("#pageError").empty();
      total = 0;
      calcTotal();
    }
    // if value does not fall in any of the if statements i.e. value is acceptable
    // remove the error message and call the calcTotal function
    $("#pageError").empty();
    total = 0;
    calcTotal();
  });
  // check if value is not empty when user exits the input
  // if empty then set value as 1, remove error message and call calcTotal function
  $("#pages").blur(function() {
    var page = $(this).val();
    if(page == ""){
      this.value = 1;
      $("#pageError").empty();
      total = 0;
      calcTotal();
    }
  });
  // Checking the subpage input (default value 0)
  // (valid value is greater than or equal to 0 but less than 10)
  $("#subpages").keyup(function() {
    var page = $(this).val();
    if(page == ""){
      this.value = "";
      return false;
    } else if(!isInteger(page)){
      this.value = 0;
      total = 0;
      calcTotal();
    }
    total = 0;
    calcTotal();
  });
  $("#subpages").blur(function() {
    var page = $(this).val();
    if(page == ""){
      this.value = 0;
      total = 0;
      calcTotal();
    }
  });
});

i do not understand why we are checking against a string value in the following condition

Because c is a character (really, a 1-character string), since that's what String.charAt returns. That said, the isInteger function could be written much more simply using a regex:

function isPositiveInteger(s)
{
    return !!s.match(/^[0-9]+$/);
    // or Rob W suggests
    return /^\d+$/.test(s);
}

or you could take another approach: convert the string to a number, make sure it's positive, and make sure that the floor of the number is the same as the original (thus it's an integer):

function isPositiveInteger(s)
{
    var i = +s; // convert to a number
    if (i < 0) return false; // make sure it's positive
    if (i != ~~i) return false; // make sure there's no decimal part
    return true;
}