
Learning the Language of Mathematics (2000) [pdf] - mutor
https://wac.colostate.edu/llad/v4n1/jamison.pdf
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jostylr
This was written in May 2000, but the following bit sounds like it was written
May 2017.

> In conclusion, I want to confess what my real goals are in teaching this
> material. In a society in which information is passed in 60 second sound
> bites and reasoning limited to monosyllabic simple sentences, careful,
> analytic thinking is in danger of extinction. And this is a grave danger in
> a democratic society beset by a host of very complex moral and social
> problems.

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cttet
"This is unacceptable because mathematics is written as English is written in
complete, grammatical sentences." Unfortunately natural languages have many
flaws and will easily falls in contradiction like Russell's paradox. Even
formal mathematical axiomatic systems encountered Gödel's incompleteness..

Maybe something like constructive category theory would give us a better way
to formally put ideas in ...

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MrManatee
The article says: 'A definition MUST be an "if and only if" statement.'

It is an established convention in mathematics to write definitions in the
form "X is Y if P(X)". For example: "A metric space M is complete if every
Caychy sequence in M converges in M".

One may question whether this is a good convention, but it is a convention
that most mathematicians tend to follow.

~~~
jordigh
That's because the other direction is implicit.

"X is a rectangle if it's a quadrilateral with all right angles."

Okay, so you can use this statement to look at an object and then check if
it's a quadrilateral with all right angles, and then conclude that, by
definition, it's a rectangle.

But for the other direction, if I tell you it's a rectangle, it's implicit
that you can conclude all right angles. Contrapositively, it's also implicit
that if I say it doesn't have all right angles, you can conclude that it's not
a rectangle, i.e. that this condition has to be satisfied for anything worthy
of the "rectangle" name.

[https://math.stackexchange.com/questions/566565/are-if-
and-i...](https://math.stackexchange.com/questions/566565/are-if-and-iff-
interchangeable-in-definitions)

------
patkai
I wish we had such a paper for programming.

~~~
walid
What's the difference? Discrete mathematical concepts are applicable to
programming as is without modification.

