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Like the Internet generally, e-mails have many advantages: they are fast (usually), cheap, and flexible, as you don't have to be at home (or work) to receive them. However, it is sometimes claimed that e-mails are completely changing the way we write.
As with the Internet, the claims run far ahead of reality. E-mails are often seen as a form of communication somewhere between a letter and a conversation. There is truth in this, but the danger is that the wrong conclusions are drawn, particularly for business e-mails.
In fact, there is much more difference in style within different types of business e-mails - and within different forms of business letters - than there is between business e-mails and business letters as a whole. Most people think of business correspondence as something very formal.
Sometimes it is - for example, when you are writing to a company or person for the first time. At the other extreme is the business correspondence with people who are also good friends. Here the language and style will be very informal - whatever the medium.
Most business communication however, falls somewhere in the middle. You are communicating - whether in German or English - with people who are “acquaintances” but not good friends. E-mails - because they are fast and frequent - encourage this communication to be somewhat more informal more quickly. If both sides are happy, there is no problem.