Why does jQuery not update the input value with $("form :input[name="some_input"]).val();

I'm trying to create a dual login script that logs a user into two separate systems (form a & form b) from another separate login (dual).

<h2>Dual Login</h2>
    <form id="dual">
    username<br>
    <input type="input" name="un" value="1234567"><br>
    password<br><input type="password" name="password"><br>
    <input type="submit" name="submit">
</form>

<h2>Login A</h2>
<form id="login_a" action="#" method="post">
    username<br>
    <input id="un_a" type="input" name="un_a" value="hi"><br>
    password<br>
    <input id="pw_a" type="password" name="pw_a"><br>
    <input type="submit" name="submit">
</form>

<h2>Login B</h2>
<form id="login_b" method="post" action="#">
    username 1<br>
    <input id="un_b" type="text" name="un_b" value=""><br>
    password<br>
    <input id="pw_b" type="password" name="pw_b"><br>
    <input type="submit">
</form>

Here is the jQuery:

$('#dual :input[name="un"]').blur(function(){
    un = $('#dual :input[name="un"]').val();
    $('#un_a').val(un);
    $('#un_b').val(un);
});

Here is a fiddle that illustrates the working example:

http://jsfiddle.net/mckinselberg/bPapQ/

My question is: Why is it that when I try to update the values this way, it doesn't work:

$('#dual :input[name="un"]').blur(function(){
    un = $('#dual :input[name="un"]').val();
    $('#form_a :input[name="un_a"]').val(un);
    $('#form_b :input[name="un_b"]').val(un);
});

Here is a fiddle that illustrates the non-working example:

http://jsfiddle.net/mckinselberg/BbKTG/