jquery function returning undefined

Hi,

I have a jscript function which I call;

var $text = runUsernameAjax('CheckUsername', 'username', $("#<%=UsernameTextbox.ClientID%>").val());
alert($text);

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function runUsernameAjax(webmethod, fieldname, fieldtext) {

            //alert('in ajax method' + webmethod + ":" + fieldname + ":" + fieldtext);

            $(function () {
                $.ajax({
                    type: "POST",
                    url: "default.aspx/CheckUsername",
                    data: JSON.stringify({ username : fieldtext }),
                        contentType: "application/json; charset=utf-8",
                        dataType: "json",
                        success: function (data) {
                            if (data) {
                                $text = "Congratulations " + fieldtext + " is available.";
                                //return text;
                            }
                            else {
                                alert("Unfortunately " + fieldtext + " is not available.");
                                return "Unfortunately " + fieldtext + " is not available.";                               
                            }
                        },
                        error: function (xhr, ajaxOptions, thrownError) {
                            return thrownError;
                        }
                    });
            });

        }

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Now am I doing something wrong as it is always returning undefined? also as I have a number of webmethods which take different values I was going to add the following but it would not work, any ideas why?

function runUsernameAjax(webmethod, fieldname, fieldtext) {

            //alert('in ajax method' + webmethod + ":" + fieldname + ":" + fieldtext);

            $(function () {
                $.ajax({
                    type: "POST",
                    url: "default.aspx/" + webmethod,
                    data: JSON.stringify({ fieldname : fieldtext }),
                        contentType: "application/json; charset=utf-8",
                        dataType: "json",
                        success: function (data) {
                            if (data) {
                                $text = "Congratulations " + fieldtext + " is available.";
                                //return text;
                            }
                            else {
                                alert("Unfortunately " + fieldtext + " is not available.");
                                return "Unfortunately " + fieldtext + " is not available.";                               
                            }
                        },
                        error: function (xhr, ajaxOptions, thrownError) {
                            return thrownError;
                        }
                    });
            });

        }

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