The Discovery of the Number e

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When most of us are first taught about the number , we are told that it is an irrational, transcendental number that is about 2.7182. Most people simply learn to manipulate . High school classes rarely mention where comes from. It is usually introduced when learning about exponents and logarithms as a “special” base that you will use a lot down the road. Early in high school I remember asking a teacher what was. I received the usual circular answer, that is the base of the natural logarithm which in turn is the logarithm of an exponent raised to the base of . This answer did not satisfy me, but I was told that I had to wait for calculus to learn other ways of approaching it’s definition...

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Note by Peter Taylor
6 years, 7 months ago

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How would you show that ee is irrational?

Note that this will heavily depend on your definition of ee.

Calvin Lin Staff - 6 years, 7 months ago

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Its simple . We write e=1+1/1!+1/2!......... and will suppose that e is rational . then e will be of form p/q . and it will be easy contradiction then

Shivang Jindal - 6 years, 7 months ago

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I tried and failed to share the blog in facebook. I guess the button right there at the right corner of the blog was for sharing on facebook!

Sheikh Asif Imran Shouborno - 5 years, 11 months ago

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