/sci/ - Science & Math » Thread #10853716

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Anonymous Thu 01 Aug 01:30:59 2019 No.10853716 View Reply Original Report

Quoted By: >>10853993 >>10854005 >>10854011

Computer, what is the significance of $e$ ?
>The number $e$ is a mathematical constant that is the base of the natural logarithm.
Computer, what is the significance of the natural logarithm?
>The natural logarithm of a number is its logarithm to the base of the mathematical constant $e$ .

Why does math education do this?

Anonymous

Anonymous Thu 01 Aug 2019 02:25:48 No.10853804 Report

Quoted By: >>10853972

Alternatively: Computer, what is the significance of $e$ ?
>The number $e$ is the unique positive real number such that $\displaystyle \frac{d}{dt}\big(e^{t}\big) = e^t$ .
Computer, why is the exponential function of base $e$ equal to its derivative?
>The derivative of $a^t$ is equal to $a^t \log{(a)}$ , and $\log{(e)} = 1$ .
Computer, why is the derivative of $a^t$ equal to $a^t \log{(a)}$ ?
> $a^t$ is equal to $e^{t\log{(a)}}$ , and the derivative of $e^t$ is equal to $e^t$ , so by the chain rule, the derivative of $e^{t\log{(a)}}$ is $e^{t\log{(a)}}\log{(a)}$ .
Fucking circular.

Anonymous

Anonymous Thu 01 Aug 2019 04:05:21 No.10853972 Report

Quoted By:

>>10853804
So it's the number at which log(x) =1. The logarithmic function is important to establish the inverse of exponentiation.

Anonymous

Anonymous Thu 01 Aug 2019 04:24:42 No.10853993 Report

Quoted By:

>>10853716
when you get to a truly elementary idea, you usually end up with some sort of circular definition.

Anonymous

Anonymous Thu 01 Aug 2019 04:33:14 No.10854005 Report

Quoted By:

>>10853716

The computer would be much better off taking you to wikipedia.

https://en.wikipedia.org/wiki/E_(mathematical_constant)

Anonymous

Anonymous Thu 01 Aug 2019 04:36:46 No.10854011 Report

Quoted By:

>>10853716
>expecting a computer to understand what you mean by "significance"

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