The number 3

VonNemo19 · #1 $Old$ July 21st, 2009, 06:25 PM

My speech teacher assigned me the topic of the number 3. It is to be a definition speech. The first thing that I thought about doing was to begin by actually "defining" in a math context the number itself. I run into a problem because some (or most) of the students in the class haven't the slightest idea of what reals, rationals, integers, wholes are, and my speech is to be only 5 minutes long. Anyone have any suggestions?

If you feel that this thread is unethical, you don't have to reply. I don't think it is though. I'm the one who still has to write and give the speech. I'm just lookin for a brainstorming session here.

billa · #2 $Old$ July 21st, 2009, 10:02 PM

I am certainly not an expert on the definition of natural numbers, but I found this

Set-theoretic definition of natural numbers - Wikipedia, the free encyclopedia

While the class (and myself) would probably not understand the motivation for defining three in this way, they could probably understand what a set is.

CaptainBlack · #3 $Old$ July 21st, 2009, 10:14 PM

Quote:

Originally Posted by VonNemo19 $View Post$

My speech teacher assigned me the topic of the number 3. It is to be a definition speech. The first thing that I thought about doing was to begin by actually "defining" in a math context the number itself. I run into a problem because some (or most) of the students in the class haven't the slightest idea of what reals, rationals, integers, wholes are, and my speech is to be only 5 minutes long. Anyone have any suggestions?

If you feel that this thread is unethical, you don't have to reply. I don't think it is though. I'm the one who still has to write and give the speech. I'm just lookin for a brainstorming session here.

I would think about something based on the Peano axioms, so three is the successor of the successor of 1.

CB

Soroban · #4 $Old$ July 21st, 2009, 11:42 PM

. . . . . $\text{Threes}$
. . $\text{by John Atherton}$

$\text{I think that I shall never }C$
$\text{A }$ # $\text{ lovelier than }3;$
$\text{For }3 < 6\text{ or }4,$
$\text{And than }1\text{ it's slightly more.}$

$\text{All things in nature comes in 3s,}$
$\text{Like }\therefore\text{s, trios, }QED\text{s.}$
$\text{While }\$\text{ gain more dignity}$
$\text{If augmented }3\times 3.$

$\text{A 3 whose slender curves are pressed}$
$\text{By banks, for compound interest.}$
$\text{Oh, would that, paying loans or rent,}$
$\text{My rates were only }3\%.$

$3^n\text{ expands with rapture free,}$
$\text{And reaches toward }\infty.$
$3\text{ complements each }x\text{ and }y,$
$\text{And intimately lives with }\pi.$

$\text{A }\odot\text{'s}$ # $\text{of }^o$
$\text{Is best }\div\text{ up by }3\text{s.}$
$\text{But wrapped in dim obscurity}$
$\text{Is the }\sqrt{-3}.$

$\text{Atoms are split by men like me,}$
$\text{But only God is 1 in 3.}$

VonNemo19 · #5 $Old$ July 22nd, 2009, 08:23 PM

Quote:

Originally Posted by Soroban $View Post$

. . . . . $\text{Threes}$
. . $\text{by John Atherton}$ ...
... $\text{Atoms are split by men like me,}$
$\text{But only God is 1 in 3.}$

That was exactly what I was looking for. Can I quote this in my presentation? Pleeeeeeeeeeaaaaaaaaaaaaaaaaaaaase?

Soroban, I've seen that you are really good with trig, have you nothing to say about that? I'd love to hear your thoughts on the majesty of the famed three sided figure...

VonNemo19 · #6 $Old$ July 22nd, 2009, 08:26 PM

Quote:

Originally Posted by CaptainBlack $View Post$

I would think about something based on the Peano axioms, so three is the successor of the successor of 1.CB

How would I ever get this across to primarily english majors? I had trouble interpreting the set theory link Billa posted (it really was exciting, though), I know that my classmates won't get it?

AlephZero · #7 $Old$ July 22nd, 2009, 09:40 PM

Quote:

Originally Posted by VonNemo19 $View Post$

How would I ever get this across to primarily english majors?

Heh. As a person who took degrees in English, math, and philosophy, I can't help but take some offense...

CaptainBlack · #8 $Old$ July 22nd, 2009, 09:41 PM

Quote:

Originally Posted by Soroban $View Post$

. . . . .
$\text{But only God is 1 in 3.}$

You cannot use this last line in an educational context any place I know since you cannot guarantee that your audience is exclusively christian (or for that matter if it were christian exclusively trinitarian).

CB

VonNemo19 · #9 $Old$ July 22nd, 2009, 09:43 PM

Quote:

Originally Posted by AlephZero $View Post$

Heh. As a person who took degrees in English, math, and philosophy, I can't help but take some offense...

None intended, I apologize. It was a stereotypical and unfair statement.

CaptainBlack · #10 $Old$ July 22nd, 2009, 09:47 PM

Quote:

Originally Posted by VonNemo19 $View Post$

How would I ever get this across to primarily english majors? I had trouble interpreting the set theory link Billa posted (it really was exciting, though), I know that my classmates won't get it?

You do some work to interpret for them in terms of counting (which is the notion that the Peano aximons is based on - ordinals rather than the set theoretic cardinals).

CB

VonNemo19 · #11 $Old$ July 22nd, 2009, 09:55 PM

Quote:

Originally Posted by CaptainBlack $View Post$

You cannot use this last line in an educational context any place I know since you cannot guarantee that your audience is exclusively christian (or for that matter if it were christian exclusively trinitarian).

CB

I agree. I would not use the last line in any setting.

AlephZero · #12 $Old$ July 22nd, 2009, 10:03 PM

Quote:

Originally Posted by VonNemo19 $View Post$

None intended, I apologize. It was a stereotypical and unfair statement.

No worries! Only having a bit of fun. We math/English scholars (yes, I have met others!) enjoy ruminating on our own absurdity.

Incidentally, were I to give such a speech, I might include something about how our usual, accustomed notion of "3" is dependent upon a very specific arithmetic system, though many others exist. (For example, we have 3=0 in systems of arithmetic modulo 3; 10+3=1 in the system of "clock arithmetic," etc.)

VonNemo19 · #13 $Old$ July 22nd, 2009, 10:26 PM

Quote:

Originally Posted by CaptainBlack $View Post$

You do some work to interpret for them in terms of counting (which is the notion that the Peano aximons is based on - ordinals rather than the set theoretic cardinals).

CB

I've known these basic axioms for years, and I had no idea that this man Peano existed, and that he set out to define the natural numbers in terms of equality. Thank you, this information is invaluable, for I am a math major, and I will soon enough be cast into the world of set logic. I feel that I have been awakened to a whole knew world. I wish I had posted this in a different forum so that I could thank you.

By the by, how do you pronounce his first name, and last name for that matter?

Swlabr · #14 $Old$ July 23rd, 2009, 12:31 AM

Quote:

Originally Posted by VonNemo19 $View Post$

How would I ever get this across to primarily english majors? I had trouble interpreting the set theory link Billa posted (it really was exciting, though), I know that my classmates won't get it?

Well, it's an easier concept to grasp than Dedekind cuts...

On the topic of "3", I saw an advert in France a couple of weeks ago, which was for a 2-for-1 offer at Disney Land. It claimed, in big letters, that 2=1. Clearly this has some major implications, the most obvious of which is that $3=2+1=1+1=2=1$ . Further, by induction, $n=1$ for all $n \in \mathbb{N}$ . So, you now know how to meet Mickey Mouse cheaply...

pomp · #15 $Old$ July 23rd, 2009, 12:35 AM

Quote:

Originally Posted by VonNemo19 $View Post$

How would I ever get this across to primarily english majors?

3 is the 'thing' that three cows, three stars, three ideas and three apples all have in common. Now you just have to define a 'thing' ...