"They're not invisible with sufficient magnification. That's how they were discovered, actually. We invented a tool called a microscope that uses lenses to magnify subjects many, many times. A guy called Robert Hooke was looking at ... um, cork, I think, and saw it was made up of a bunch of tiny building blocks. Of course, in a cork they were dried out and not alive, but he identified the basic structure. As for what they do, it depends on what kind they are. Complex plants and animals are built of a ton of different cell types -- cells make up your skin or your hair or your blood or whatever. Some organisms are just one cell - organisms that give people food poisoning, for example."
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