There is a pattern here: In each age of computing, individual machines begin as single-user systems. They are eventually joined into networks and later blend together, as if they've become one big system.
When early computers first formed wide area networks, it was to allow users on one machine access to others. A mainframe user at his or her terminal could log in to another mainframe in the same building or halfway around the world, accessing data, generating reports, and running applications toward their own goals, as long as their access was authorized. Later, loosely coupled mainframes presented common job and print queues. These were the inputs and outputs of a big computer, and in that sense the interconnected machines presented a single-system image to the user.
Minicomputers had a short life, being quickly overtaken by engineering workstations, which were similarly shoved aside by the personal computer, which became more powerful over the years. When PCs first formed local area networks, it was to allow users access to a printer and a central file and application server. Later, after IVY and Beowulf made their marks, the Pile-of-PCs became fused into a single system image; first as a supercomputer (such as IVY and Beowulf), then as a cluster server, and lately as a Web server.
PDAs began as a single-user, hands-on devices, just as mainframes, minicomputers, workstations, and PCs did. They became terminals, allowing their users access to the Internet, but they have yet to form a network among themselves, presenting a single-system image. But that is clearly on the horizon.