Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2014-05-17 04:21:40

ShivamS
Member
Registered: 2011-02-07
Posts: 3,557

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.

Offline

#2 2014-05-17 04:27:18

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,176
Website

Re: More rigorous definitions

There are other sites for rigorous definitions..


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#3 2014-05-17 04:28:39

ShivamS
Member
Registered: 2011-02-07
Posts: 3,557

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.

Offline

#4 2014-05-17 04:46:56

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,176
Website

Re: More rigorous definitions

Why do we need the formal definition?

bobbym wrote:

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#5 2014-05-17 04:52:28

ShivamS
Member
Registered: 2011-02-07
Posts: 3,557

Re: More rigorous definitions

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

Offline

#6 2014-05-17 06:13:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,247

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.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#7 2014-05-17 06:19:53

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,426

Re: More rigorous definitions

hi ShivamS

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

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#8 2014-05-17 11:55:59

ShivamS
Member
Registered: 2011-02-07
Posts: 3,557

Re: More rigorous definitions

Agnishom wrote:

Why do we need the formal definition?

bobbym wrote:

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.

bob bundy wrote:

hi ShivamS

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

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)

Offline

#9 2014-05-17 19:20:31

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,426

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


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#10 2014-05-18 00:12:57

ShivamS
Member
Registered: 2011-02-07
Posts: 3,557

Re: More rigorous definitions

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

Offline

#11 2014-05-18 00:21:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,247

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

Board footer

Powered by FluxBB