# Smargest number

1. Dec 14, 2004

### tribdog

What is the:
smallest # whose definition requires at least 50 symbols?

2. Dec 14, 2004

### jcsd

seventy-five?

3. Dec 14, 2004

### tribdog

that is only 12 symbols
and could also be written:
75-2symbols
3(5^2)-6symbols
70+5-4symbols

Last edited: Dec 14, 2004
4. Dec 14, 2004

### chroot

Staff Emeritus
I understand this is supposed to be a brain teaser, but is it meaningful without precise explanation of the terms "definition" and "symbol?"

- Warren

5. Dec 14, 2004

### jcsd

It's an old so-called paradox, I can't remember who thought of it now, but the paradox is that if there exists such a number you can always define it by "the smallest # whose definition needs at least 50 symbols", which is less than 50 symbols

6. Dec 15, 2004

### DaveC426913

disqualified

jcsd, did you mean: ('...which is at least 50 symbols'? That's what the question was asking for.

BTW, I count 56. No reason not to count the spaces.
)

Too bad this answer is invalid (even if it is the intended answer). What it has created is:

(The smallest # whose definition requires at least 50 symbols is 'the smallest # whose definition requires at least 50 symbols'.

This is a circular argument. It doesn't mean anything.

What is 1?
1 is the number defined as 1.
)

7. Dec 15, 2004

### jcsd

I meant exactly what I wrote.

Do you understand the concept of a paradox :uhh:

8. Dec 15, 2004

### Gokul43201

Staff Emeritus
I think the confusion between what you (jcsd) meant and how DaveC interpreted it lies in the "number of symbols". Clearly, the 'number of symbols' refers to the number of different symbols, while, I believe, DaveC's counting the total number of characters in the definition.

9. Dec 15, 2004

### RoseMary

In that equation there are 49 symbols...

s m a l l e s t # w h o s e d e f i n i t i o n r e q u i r e s a t l e a s t 5 0 s y m b o l s ?

10. Dec 15, 2004

### Hurkyl

Staff Emeritus

11. Dec 18, 2004

### DaveC426913

Rosemary, why don't you consider the space as a symbol?

12. Dec 18, 2004

### DaveC426913

"Do you understand the concept of a paradox."

I do. Do you? A paradox would require 2 apparently true statements that appear to contradict each other. This is not a paradox, it's merely incorrect.

Say we agree that the definition is "the smallest # whose definition requires at least 50 symbols".

You state that this *is* less than 50 symbols (after all, you meant what you wrote). If it is less than 50 symbols, then it is clearly an incorrect definition. The statement is false, there is no contradiction, there is no paradox.

That big said, according to *my* interpretation (counting spaces), the definition *is* at least 50 symbols. It is not contradicting itself.

But what I'm saying is the answer isn't an anser at all.

"The smallest number whose definition requires at least 50 symbols can be defined as 'The smallest number whose definition requires at least 50 symbols'".

is not an answer. Just as '1 is defined as 1' is not an answer.