Q:

How to display an array to the user

I'm trying to display the contents of an ordered array in something like a JTextField.
for (int i=0; i<array.length; i++) {
    this.textField.setText(array[i]);
}

This won't work for two reasons. The first minor reason: if the array length is 4 then jtextfield is getting it's value reset 4 times rather than appending each element onto the last.
Second reason: The JTextField only takes strings. I can't find anything I can use in Swing that will let me display integers to the user. Any help?

A:

Quick & Dirty Answer
for (int i=0; i<array.length; i++) {
    this.myJTextField.setText(this.myJTextField.getText() + ", " + array[i]);
}

Correct Way
First, calling a member variable JTextField probably isn't wise. Since the class is already called like that, it will confuse readers. Naming conventions in Java state member variables are like myTextField for example. (note: original question changed).
User defined format
Note you can convert any number to a string by simply doing "" + number too. If you have many strings, consider using a string builder, as that's faster and won't update the GUI element multiple times: (also fixes the initial ", " before the first item, which happens above)
StringBuilder builder = new StringBuilder();
for (int i=0; i<array.length; i++) {
    builder.append(array[i]));
    if(i + 1 != array.length) 
        builder.append(", ");
}
this.myJTextField.setText(builder.toString());

Canonical array representation
Alternatively, you can use this:
this.myJTextField.setText(Arrays.toString(array));

It will look like [1, 4, 5, 6].

