10 hour efforts failed: [Ajax response into $(div).html] DOESN'T work

10 hour efforts failed: [Ajax response into $(div).html] DOESN'T work

If I set $_SESSION[''] in php file, it works on index7.php. But I want to know it can work using Ajax response.


[question] What I want is just to make $("#letters").html("fjejief") work.

  cf. Please change the extensions of attached files from .txt to .php.
  
My guess: Ajax and session and show() are messed up with each other.


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index7.php -> signin_process7.php -> index.php
-=====================================================



var jdata = {'email1':email1, 'user_password':boxpassw1};
                                                     
                    $.ajax({
           type: 'POST',
           url: 'signin_process.php', 
           data: jdata,
           cache:false              
       })
       .done(function(data){
        if(data){
               
       
     
                                            $(".mainindex").show(); <--(This class includes #letters)                                 
                                   
          $("#letters').html('kdjfkjkefe');  <-- This doesn't work!
 }else{