[jQuery] Issue with setting click event functions in a for loop

[mikfig]

I have a webpage that searches a database using a php script to search
the database and a jQuery app on the page to retrieve the results and
show them. So it works fine, but then I want to add page number
buttons to allow the user to go to different "pages" of the results.
So I have a DIV with the id of "page_buttons" and I use the following
code: http://pastebin.com/m3dffbf99

I use the offset and the results per page like this in a MySQL query
in the php script: SELECT .... LIMIT offset,
resultsPerPage by the way.

So anyways, the problem I am having is that if I have a loop like
this:

var pageNum = 6;
...
for(var i = 0; i <= pageNum; ++i)
{
    $("#page" + i).click(function() { alert('page ' + i + '
clicked.'); });
}

The elements with IDs of "page1", "page2",... are buttons, and I
tested the above loop. What happens is if I click any of the buttons
with IDs of "page1", "page2",.. then they all "alert" with the string
"page 7 clicked". All the page buttons 1-6 display the string "page 7
clicked".

To try to greater understand this problem I took the functionality out
of the loop like this:

var i = 2;
$("#page" + i).click(function() { alert('page ' + i + '
clicked.'); });
i = 3;
$("#page" + i).click(function() { alert('page ' + i + '
clicked.'); });

and it worked just fine with "page2" alerting "page 2 clicked and
"page3" alerting with "page 3 clicked".

So I was hoping someone could help me in explaining why this issue
occurs and if there was a better way to do what I'm trying to do.

Thanks,
mikfig