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newton1
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we know e (exponential) is a irrational number...
how can we prove it??
how can we prove it??
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e*j!= integer+ 1/(q+1)+ 1/(q+1)(q+2)+ ... which is not an integer
An irrational number is a real number that cannot be expressed as a ratio of two integers. This means that it cannot be written as a simple fraction, and its decimal representation is non-terminating and non-repeating.
e, also known as Euler's number, is a mathematical constant that is approximately equal to 2.71828. It is a fundamental constant in calculus and is often used in exponential growth and decay equations.
The proof that e is an irrational number was first given by Swiss mathematician Leonhard Euler in the 18th century. It involves using the properties of limits and infinite series to show that e cannot be expressed as a ratio of two integers.
Knowing that e is irrational is important in mathematics because it allows us to use it as a base for logarithms and exponential functions. It also has applications in fields such as physics, engineering, and finance.
Yes, there are several other irrational numbers that are related to e, such as pi (π) and the golden ratio (φ). These numbers have their own unique properties and are also commonly used in mathematical equations and formulas.