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Showing posts from July, 2018

Are There?

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A note fron "Contemporary Abstract Algebra - J.A. Gallian (8th Edition) "I was interviewed in the Israeli Radio fir five minutes and I said that more than 2000 years ago, Euclid proved that there are infinitely many primes. Immediately the host interrupted me and asked: "Are the still infinitely many primes?"                                                                 -Noga Alon

Happy 'e' - day

Hello friends , Today is 2nd of July , 2018 that is 2-7-18 (2.7.18). We know 'e' as Euler's number/ The Value of 'e' : 'e' is an irrational number with value            e = 2.718... The few digits are: 2.7182818284590452353602874713527.... It is often called Euler's number after Leonhard Euler (Pronounced "Oiler"). 'e' is the base of the Natural Logarithms which was invented by "John Napier". Calculating : There are many ways of calculating the value of e , but none of them ever give a totally exact value, because e is irrational. But it is known to over 1 trilllion digits of accuracy. For example, the value of $(1 + \frac{1}{n})^n$ approaches e as n gets bigger and bigger. i.e.$e = \displaystyle  \lim_{n\to\infty}(1+ \frac{1}{n})^n $ Another Calculation : The value of e is equal to $\frac{1}{0!} +\frac{1}{1!} +\frac{1}{2!} +\frac{1}{3!} +\frac{1}{4!} +\frac{1}{5!} +\frac{1}{6!} +\fr...