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### Number e

With the number e = 2,7182… you can calculate just as well as with all other numbers.

##### Explanation

The exact value can be written as a limit

or with a series development as

Those calculations give the value e = 2.7182… where you can determine the accuracy yourself. The decimal numbers never create a pattern that repeats itself. The number e is comparable to π where this is also the case. That is why these two numbers are called transcendent.

You cannot write the number e as a fraction. That is not so exceptional, because you cannot write as a fraction either. On the other hand, the number

that also has an infinite number of decimal places. In a division you see clear similarities

and the same result gives

The number e has a place on the number line, and of course lies between the integers 2 and 3, so

##### History

The mathematician Charles Hermite proved in 1873 that the number e is transcendent.