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How can the electromagnetic can travel in air and not lose any information contained in them?


There is a limit to how far you can get television signals. The power is spreading out the farther you are away from the source. At some distance, you reach a point where the noise in the atmosphere becomes greater than the signal, and you can no longer extract all the information from the signal. Digital television has much error correction, many bits are sent just so corrections can be made when there are errors. This helps on the fringe, but even this fails when the signal gets weak enough. However, error correction makes the signal perfect until you hit that exact point where the correction fails. Thus, digital TV has a sharp cutoff point - you get a perfect picture, or it goes away completely. Therefore, electromagnetic waves do lose information. Think of someone aiming a flashlight at you. The person walks further and further away from you. At some point, you are just not going to be able to tell. What if there were fogs or lots of pollution in the air? Alternatively, 20 other flashlights and you had to pick out just the one. It is easy and 100% when they are close.

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