# Are You Sure One And One Makes Two?

1. Apr 2, 2004

### deda

How much chewing gums you get by adding one to another?

2. Apr 2, 2004

### matt grime

Not a new thought, in essence. Go and read Whitehead and Russell for a bit of light entertainment.

The simplest refutation/explanation of this is: what do you mean by add? Pick up one stick of chewing gum, now pick up another? How many sticks have you picked up there? That kind of 'addition' is different from putting two pieces in your mouth and chewing. It's not a difficult philosophical argument to have, it just requires you to think about the words you are using.

Last edited: Apr 2, 2004
3. Apr 2, 2004

### Chen

Two of course.

4. Apr 2, 2004

### Shahil

Doesn't matt grime's post bring up an interesting topic? Does the chewing gum problem mean that there exists another branch of mathematics hich WILL solve the two pieces uh...riddle?

5. Apr 2, 2004

### matt grime

In the arithmetic of cardinals aleph-0 + aleph-0 = aleph-0

Or how about a quote from Blackadder II (the one with kate, short for bob)

Edmund Blackadder:So, Baldrick, if I have two beans and I add two more beans, what do I have?
Baldrick: A very small casserole.

Last edited: Apr 2, 2004
6. Apr 2, 2004

### Organic

First we have to know what is 1 before we add 1 to 1.

For example:

The notation of the empty set is {}, which means that nothing is included between '{' and '}'.

The cardinal of {} is 0 and it is notated like this: |{}|=0

The notation of a non-empty set is {x}, which means that at least some singleton is included between '{' and '}'.

The cardinal of {x} is 1 and it is notated like this: |{x}|=1

Let us say that x=1/2.

Now we have two basic possibilities:

a) The absolute approach:

|{x}|+|{x}|= 2 it means that we ignore the value of singleton x.

b) The relative approach:

If x=1/2 then x+x = 1
If x=1/4 then x+x = 1/2
If x=1/8 then x+x = 1/4
...

But be aware that there is already some 1 in our calculations; otherwise we cannot calculate 1/2, 1/4, 1/8 and so on.

In the case of the chewing gums, the result is 2 by (a) approach,
and can be any other result by (b) approach, if our 1 is already known.

But there is another possibility:

c) 1 property is unknown therefore we cannot write 1+1 = x,

But we can write x+x = 1.

Therefore by (c) x is included in 1.

Last edited: Apr 2, 2004
7. Apr 2, 2004

### matt grime

Erm, Organic, sorry to start off again, but the cardinality of the set {x} where x is a single element of some kind is independent of what x is.

8. Apr 2, 2004

### Organic

I know, and I also wrote it in my previous post. See the absolute approach.

9. Apr 2, 2004

### matt grime

Then what was the point of your post? Apart from to pormote your ignorant postition of mathematics again?

10. Apr 2, 2004

### Michael D. Sewell

It seems vague, but is in fact meaningless.-Dick Van Dyke

11. Apr 2, 2004

### BookWorm

I will awnser that question if you, or anyone, can give me 1/2 of a piece of chalk.

12. Apr 2, 2004

### Michael D. Sewell

BOOKWORM FOR PRESIDENT!!!!!

13. Apr 2, 2004

### Integral

Staff Emeritus
Speaking of chalk,

why does a full stick of chalk break into PI pieces when dropped?

14. Apr 2, 2004

### chroot

Staff Emeritus
ROFLMAO, BookWorm... that sounds like something Feynman would have said.

- Warren

15. Apr 2, 2004

### BookWorm

What do you mean by a full stick of chalk? They come in so many different sizes.

16. Apr 2, 2004

### Michael D. Sewell

SO DOES CHEWING GUM! THAT'S THE ANSWER!!!

17. Apr 2, 2004

### chroot

Staff Emeritus
Man, I've never seen Michael quite this excited before!

- Warren

18. Apr 2, 2004

### Michael D. Sewell

No one ever made it so easy before. This is rich.

19. Apr 2, 2004

### BookWorm

Ooops, I didn't mean to give it away like that. Hope no one has been trying to figure that one out for to long. They could be a little upset that a kid awnsered it in just a few minutes.

Sorry,
The kid who reads to much.

20. Apr 2, 2004

### Michael D. Sewell

I got dis idee for a car see, you draw pullusion thru thi exsauhst an blow it out ef the karberator an it manufactures gasoleen. Also it draws heat out of thi atmosfeer wid the radiatur. DON'T even try to tell me it won't work, I seen one.

Last edited by a moderator: Apr 3, 2004