Is it possible to use web development tools and create an actual working WYSIWYM math editor, like desktop Applications such as MathType?

Before I started to try and make this thing, I wanted to know if it is possible, under the following circumstances:

• The code to script up that math must be able to be taken, submitted and stored in a database
• The code for two pieces of math which look exactly the same must have the exact same code
• According to the requirements, wherever the user clicks his or her mouse, the caret must move to that specific element or part of the math

So, is it possible? I'm looking forward to using technologies such as HTML, JavaScript, jQuery, and even Flash as a last resort.

MathQuill lets you type maths in a WYSIWYG fashion, source here. There is a demo on the homepage.