Ajax is used in web development and is a programming/web designing language. You could search wikipedia for that: wikipedia.org/wiki/Ajax_(programming) HTML:
AJAX is not a language, it's a method of using Javascript and a server-side language to enable two-way communications between the client and the server. It's used to send data to the server and/or from the server to the client, without having to refresh the page.
I agree, AJAX is not a language, but it is not a method of using Javascript either. It is part of the jquery library, which is a javascript (ECMA script) implementation. Also, you contradict yourself by saying that it is "a server-side language" - it is not a server-side language. Then again, I agree with the rest of the statement - it is a way to "trick" the communication model where the client has to send a request to the server to receive a reply. You can have different javascript triggers trigger AJAX calls that go and get information from the server (usually from the database), and returns the result without even refreshing a page. This way you can dynamically change content on the page, executing some server-side logic.
True, but that's not part of the definition, any more than "rubber" is part of the definition of "car", even though rubber is part of a car (the tires) jQuery is a Javascript library, it's not an ECMAscript implementation. (An ECMAscript implementation is the Javascript interpreter in your browser, or the JScript interpreter, if you use IE.)