jQuery serializeArray doesn't include the submit button that was submit - php

Question

I was trying to send a form data to php code some how when I have condition of if the button was submit do the following code it doesn't work :
$("button#send").click(function() {
var error = '';
var send = $("#send").val() = true;
if ($('#username').val().length == 0) { error += 'user name<br />'; }
if ($('#password').val().length == 0) { error += 'password<br />'; }
if ($('#repassword').val().length == 0) { error += 'repassword<br />'; }
if ($('#password').val() != $('#repassword').val()) { error += 'pass match<br />'; }
var phonenum = $('#phonenum').val() + $('#select').val();
if (phonenum.length == 0) { error += 'phone num <br />'; } else if ($.isNumeric(phonenum) == false || phonenum.length != 10) { error += 'phoneworng<br />'; }
if (error != '') {
$('#result').html(error);
} else {
$.ajax({
url: $("#form_reg").attr('action'),
data: $("#form_reg input").serializeArray(),
type: 'POST',
success: function(result) {
$("#result").html(result);
},
error: function(error) {
alert(error);
}
});
}
$("#form_reg").submit(function(e) {
e.preventdefault;
return false;
});
});
here the html code
<form id="form_reg" action="AddUser.php" method="post">
<div class="head_div"> <span> reg </span> </div>
<div id="main_reg">
<div class="login_line">
<label for="username">username</label>
<input type="text" name="username" id="username" placeholder="username" />
</div>
<div class="login_line">
<label for="password"> passs </label>
<input type="password" name="password" id="password" placeholder="pass" />
</div>
<div class="login_line">
<label for="repassword"> repass </label>
<input type="password" name="repassword" id="repassword" placeholder="repass" />
</div>
<div class="login_line">
<label for="email"> email </label>
<input type="email" name="email" id="email" placeholder="email" />
</div>
<div class="login_line">
<label for="phonenum"> phone num</label>
</div>
<div class="login_line">
<input type="text" id="phonenum" name="phonenum" placeholder="phone num" />
<select id="select">
<option value="050"> 050</option>
<option value="054"> 054</option>
<option value="052"> 052</option>
<option value="053"> 053</option>
<option value="058"> 058</option>
</select>
</div>
</div>
<div class="login_line">
<div id="result"> </div>
</div>
<div class="send_line">
<button type="submit" name="send" id="send"> reg</button>
</div>
</form>
here the php
include_once 'login_db.php';
$error_msg="";
if(isset($_POST['send']))
{
And the rest there include the echo somehow without the if isset($_POST['send'])
the code is echo the result