I'm not sure if you mean the foundation of Mac OS X itself, or of the desktop. The desktop is a part of Mac OS X's Finder application which is written by Apple from scratch in Objective-C using the Cocoa framework. Mac OS X itself's core is Darwin, a UNIX operating system based on the open source FreeBSD.
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There are no viruses affecting Mac OS X.
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OS X is an operating system. It is ran by Intel if you are asking that.
Mac OS X is pronounced Mac OS Ten. It follows on from Mac OS 9 which was the last version of what is now known as the classic Mac OS and it saw the introduction of the new UNIX based OS so the Roman numeral X was adopted to mark the change.
It depends what you mean by 'introduced'. Mac OS X Server 1.0 was released in 1999 but I imagine you are referring to the first desktop OS to use this technology; the first public beta was released 2000 but the first full desktop release was in 2001.
The second name of Mac OS X v10.4.5 is Mac OS X v10.4 Intel.Mac OS X 10.4 was known as Mac OS X Tiger.
Mac OS X 10.4 (Tiger) needs to be purchased as it is not possible to update from Mac OS X 10.2.8
Mac OS X is an operating system released by Apple Inc. It is designed for Apple branded computers, which is why you will never see a Dell, or an HP computer run Mac OS X. There are only two important versions of Mac OS X, Mac OS X Server, and regular Mac OS X. Mac OS X server was designed for servers, while regular Mac OS X was designed for most computers. The current version of Mac OS X (10.6) is named Snow Leopard.
Yes, it is. Any type of MacBook that comes out now is a Mac OS X. The most recent version of Mac OS X is Mac OS X Lion, coming out soon.
Mac OS X uses Darwin.
Mac OS X is based on UNIX.