definition of e
In mathematics, the number e, also known as Euler’s number, is a fundamental mathematical constant approximately equal to 2
In mathematics, the number e, also known as Euler’s number, is a fundamental mathematical constant approximately equal to 2.71828. It is named after the Swiss mathematician Leonhard Euler, who made significant contributions to the field of mathematics and its applications.
The number e can be defined in several ways. One common definition is as the limit of the expression (1 + 1/n)^n as n approaches infinity. In other words, as the value of n becomes larger and larger, the exponentiated expression (1 + 1/n) becomes closer to the value of e.
Another definition of e is as the sum of the infinite series 1 + 1/1! + 1/2! + 1/3! + …, where n! (read as n factorial) is the product of all positive integers from 1 to n. This series converges to a finite value, which is e.
The number e is an irrational number, which means it cannot be expressed as a fraction or ratio of two integers. It has many important applications in various areas of mathematics, including calculus, exponential growth and decay, and complex analysis. It also shows up in various real-world phenomena, such as compound interest calculations in finance and exponential growth patterns in population dynamics.
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