The Discovery of the Number e

Main post link -> http://blog.brilliant.org/2013/02/17/the-discovery-of-the-number-e/

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...

Read the rest over at the blog.

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Comments

How would you show that $e$ is irrational?

Note that this will heavily depend on your definition of $e$ .

Calvin Lin Staff - 8 years, 3 months ago

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 - 8 years, 3 months ago

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 - 7 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$