How can I check if a checkbox is checked?

I am building a mobile web app with jQuery Mobile and I want to check if a checkbox is checked. Here is my code.

<script type=text/javascript>
  function validate(){
    if (remember.checked == 1){
      alert("checked") ;
    } else {
      alert("You didn't check it! Let me check it for you.")
    }
  }
</script>

<input id="remember" name="remember" type="checkbox" onclick="validate()" />

But for some reason or another it doesn’t execute it.

Please help !

—-EDIT—–
This is what I have for the moment.

<DIV data-role="content" data-theme="g">
    <DIV class=ui-grid-g-login>
        <FORM method=post action=[$=PROBE(266)/] data-theme="C">
            <P>~DATA_ERROR~</P>
            <div id="mail" data-role="fieldcontain">
                <label for="mail">Email:*</label>       
                <input id="mail" name="mail" type="email" />
            </div>
            <div id="pass" data-role="fieldcontain">
                <label for="pass">Paswoord:*</label>        
                <input id="pass" name="pass" type="password" />
            </div>
            <div id="remember" data-role="fieldcontain">
                <label for="remember">Onthoud mij</label>       
                <input id="remember" name="remember" type="checkbox" onclick="validate()" />
            </div>
            <P><INPUT class=btn name=submit value=Login type=submit  onclick="validate()"></P>  
        </FORM>
    </DIV>
</DIV><!-- /content -->

<script type=text/javascript>
function validate(){
    var remember = document.getElementById('remember');
    if (remember.checked){
        alert("checked") ;
    }else{
        alert("You didn't check it! Let me check it for you.")
    }
}
</script>

—-EDIT–

Solved it, the problem was that the fieldcontain was also named ‘remember’