Math Is Fun Forum

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

More rigorous definitions

For the pages at MIF, why not have a more layman-type definition and a rigorous one? For example, there are set theory tutorials on MIF, so why not cover the rigorous definition of a function and relation? You might want to add a page regarding Cartesian products in the set theory tutorials first.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: More rigorous definitions

There are other sites for rigorous definitions..

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: More rigorous definitions

To be honest, that isn't really a valid counterpoint. There are also other sites which provide mathematics tutorials. I meant not to just provide the definition, but explain it a little.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: More rigorous definitions

Why do we need the formal definition?

Anything formal is useless.

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: More rigorous definitions

To understand mathematics better. And it is a requirement in further mathematics.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: More rigorous definitions

I believe the quote is

Anything rigorous is meaningless

it was said by Rene Thom. It is not necessarily my viewpoint on rigor.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: More rigorous definitions

hi ShivamS

There's nothing to stop you making such a page(s). 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: More rigorous definitions

Why do we need the formal definition?

Anything formal is useless.

You do not like rigorous mathematics? That's probably because you haven't been exposed to a lot of it, but most of university mathematics is intuition/motivation -> definition -> derivation -> proof/other justification -> examples/application. There, everything is formal and you usually won't be given analogies like "a function is a machine," which is the popular one with functions.

hi ShivamS

There's nothing to stop you making such a page(s). 

Bob

I am not MIF.

On a side note, what stage do you teach? I think you mentioned AS/A level some time ago.

Last edited by ShivamS (2014-05-17 11:56:56)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: More rigorous definitions

hi ShivamS

My training is for ages 11-18, but I have also taught younger and the occasional college student.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: More rigorous definitions

I also had a dream that bobbym posted in this thread saying his viewpoint on rigor!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: More rigorous definitions

He might have, but I usually do not pay much attention to what he says.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.