Jquery Validation Rules for comparing two numbers

Question

I have these two Input boxes

form_open('performances/save/'.$performance_info->prf_id,array('id'=>'performance_form'));

    form_input(array(
            'class'=>'beg_inv',
            'name'=>'beg_inv',
            'id'=>'beg_inv',
            'value'=>$performance_info->beg_inv);

    form_input(array(
            'class'=>'end_inv',
            'name'=>'end_inv',
            'id'=>'end_inv',
            'value'=>$performance_info->end_inv);

form_submit(array(
    'name'=>'submit',
    'id'=>'submit',
    'value'=>$this->lang->line('common_submit'),
    'class'=>'submit_button float_right')
);

and i am using this jquery validate:

$('#performance_form').validate({

    submitHandler:function(form)
    {
        $('#prf_id').val($('#scan_performance').val());
        $(form).ajaxSubmit({
        success:function(response)
        {
            tb_remove();
            post_exp_form_submit(response);
        },
        dataType:'json'
    });

    },
    errorLabelContainer: "#error_message_box",
    wrapper: "li",
    rules:
    {
        prod_id:"required",
        beg_inv: { greaterThan: "#end_inv" }


    },
    messages:
    {
        prod_id:"<?php echo $this->lang->line('performances_product'); ?>",
        beg_inv:"<?php echo $this->lang->line('performances_qty_val'); ?>"

    }
});

I used the greaterThan as I have seen in this url but that is for dates only I think because my code above does not work. What is the equivalent of the greaterThan for numbers? Or are there any?

EDIT:

adding this worked out, new question: How do I Validate again when I corrected the end_inv without going back to the beg_inv to trigger the rule. If I add a new rule it will create a new error line instead of overwriting the first error message. Fiddle here by Riley

$.validator.addMethod(
    "greaterThan",
    function (value, element, params) 
    {
        var target = $(params).val();
        var isValueNumeric = !isNaN(parseFloat(value)) && isFinite(value);
        var isTargetNumeric = !isNaN(parseFloat(target)) && isFinite(target);
        if (isValueNumeric && isTargetNumeric) {
            return Number(value) > Number(target);
        }

        if (!/Invalid|NaN/.test(new Date(value))) {
            return new Date(value) > new Date(target);
        }

        return false;
    }, 'Must be greater than {0}.');