In space, sound cannot travel because there is not enough air. Space is a nearly perfect vacuum. The few stray molecules floating about in space are much too far apart to propogate sound waves. Space is also very cold - its average temperature is only fractionally above absolute zero.
In the United States, there is no legal definition for "space;" however, a crew member of a government vehicle is considered an astronaut if they have been above 50 miles in altitude above mean sea level. This definition of astronaut leads to a common acceptance of "space" in legal documents as beginning at 50 miles in altitude.
The USA is not the only country to lack a legal definition of outer space; however, one common definition in countries which use the metric system is the Kármán line, which labels "space" as anything about 62.1 miles in altitude.
Signatories of the so-called Outer Space Treaty have agreed not to test nuclear weapons in space, or claim land in outer space as sovereign territory. 
The ancient Greeks debated whether space was finite or infinite. The ancient Greeks recognized that it was difficult to imagine what an infinite universe might look like. But they also wondered that if the universe were finite, and you stuck out your hand at the edge, where would your hand go? The Greeks' two problems with the universe represented a paradox - the universe had to be either finite or infinite, and both alternatives presented problems. 
- The Expanding Universe, Sloan Sky Survey