Plot derivative of a function

[Manolo Sobrino]

(06-06-2014 08:24 AM)cyrille de brébisson Wrote:  Hello

> Math will never be confusing

I beg to differ!

Math is extremly confusing. Past the very basic things (and even then...), most definitions are not agreed upon between mathematicians, and they all play with slightly different, generally unspoken rules depending on their field and even locale.

Examples:
- -6 is a number (a negative number) the square of a number is the number times the number. and yet -6² is -36!

- 3 points at the same location is a triangle... or not, depending on where you are from

- depending on your locale, in right to left writing countries, PI is written 3.14159 or 95141.3 your job to figure out which number is actually ment (PI is easy, but if you read 1.5, you do not know if it is 1.5 or 5.1!)

- 0^0 is undefined or 1 (some other say 0, but they are a minority)

- Matrix + scalar is mathematicaly non-sensical.. even then, I have seen it often, both in math packages and in math texts to say: add scalar to every item in the matrix.

- Modulo is not formally defined (at least not in a consistent manner) for negative numbers.

- Addition is not associative in numerical math!

etc, etc, etc...

These are all mathematic confusion which, when you move from one part of math to another cause confusions, errors and mis-understanding... In our field, where do do touch multiple levels, locals, type of users, we see this all the time...

Cyrille
Un-Obfulscating since 1998

People are confusing, Maths are not (just undecidable sometimes), unless you confuse Maths with the conventions used to write them down. You should always choose a consistent one. And writing that kind of integrals is a bad convention, which besides is formally wrong. Neither Riemann nor Lebesgue would know what to do about such a beast and you're doing Riemann.

Your examples... -6, everybody understands that -6 is -6, and -6^2 is -36 (unless you confuse good old written on blackboards Maths with RPN). If they wanted it to be 36 they'd have written (-6)^2. 3 points at the same location are whatever you want them to be, but mainly they are the same point unless we're not talking about Geometry. You can write left to right or right to left, but if you want to publish your results you will write Pi=3.14159265... 0^0=1 is as convenient as 0!=1 is, but it really doesn't matter. Keeping it indeterminate is possibly even better. Modulo of a negative number, it doesn't matter how you define it as long as you're consistent with it and the rest of remainders. Addition of Real numbers is associative in Numerical Maths, it's not for floating point numbers on finite precision devices, so what? You can do numerical analysis with a stack of paper and a pencil, that's how they made it first.

After having read some of the musings and questions about Maths of calculator designers I just understand calculators so much better... you won't catch a Mathematician saying that Maths are confusing. BTW, would you trust a doctor who says that Medicine is confusing?