Is this a paradox?

bunny · #1 07-18-2007, 07:55 PM

People make reference to numbers all the time in everyday speech, in articles, journals and so on (not references to a class as in "all odd numbers" but individually like "17", "a googol", "the smallest perfect number greater than 1000", etcetera). Someone made the comment to me the other day that not all numbers will be referenced by a human being, there just isnt enough time to cite an infinite number of numbers. Given that, it seemed to me that there must be a smallest natural number which will never be referenced by a human being. Having said that, havent I just referenced it?

Anyone know if this has a name (or if I'm just making a simple thing complicated - I've been mulling it over for days now and I'm all confused...)

Nielsio · #2 07-18-2007, 08:08 PM

You referenced the concept, not the number itself. Clearly that number keeps moving like a whack-a-mole type thing.

Personally I couldn't really care. This concept is of no use whatsoever.

bunny · #3 07-18-2007, 08:37 PM

[ QUOTE ]
You referenced the concept, not the number itself. Clearly that number keeps moving like a whack-a-mole type thing.

[/ QUOTE ]
Possibly - one solution seemed to me to be that the number was undefined.

[ QUOTE ]
Personally I couldn't really care. This concept is of no use whatsoever.

[/ QUOTE ]
I found it strange that you would say this. Firstly, I dont see the point in wasting the time to reply to some post if you really dont care. But mainly it's the second comment. Do you really expect to be able to tell how useful a concept right from the moment you read it? Most pure maths results are of completely no use when they first crop up - they usually only become "useful" much later. It would seem to me to be a shame if we should stop doing research into or thinking about anything which wasnt immediately seen as useful.

pleasefish · #4 07-18-2007, 08:40 PM

This is similar to the interesting number paradox.

However, I can reference all of the natural numbers (I just did). [img]/images/graemlins/laugh.gif[/img]

bunny · #5 07-18-2007, 08:50 PM

Yeah, my friend excluded referencing a class of numbers together. He was restricting himself to instances where the speaker referenced only one number at a time.

Thanks for the interesting number reminder. That is pretty much the same, though "interesting" seems less well defined than "referenced by a human at any time".

kerowo · #6 07-18-2007, 08:51 PM

What do you mean by reference? Because in the sense you are using you have already referenced all numbers in your preamble. If you mean "state the actual number a convient short hand for that particular number" than no it isn't because you cannot know that particular number like with your other examples.

bunny · #7 07-18-2007, 08:53 PM

Again, referencing a singular, specific number, not instances which refer to several numbers at once (ie all integers). Some examples: "The smallest prime greater than 100", "the product of the fist 100 primes", "the perfect number between 10 and 50", etcetera...

Nielsio · #8 07-18-2007, 09:13 PM

[ QUOTE ]
[ QUOTE ]
You referenced the concept, not the number itself. Clearly that number keeps moving like a whack-a-mole type thing.

[/ QUOTE ]
Possibly - one solution seemed to me to be that the number was undefined.

[ QUOTE ]
Personally I couldn't really care. This concept is of no use whatsoever.

[/ QUOTE ]
I found it strange that you would say this. Firstly, I dont see the point in wasting the time to reply to some post if you really dont care. But mainly it's the second comment. Do you really expect to be able to tell how useful a concept right from the moment you read it? Most pure maths results are of completely no use when they first crop up - they usually only become "useful" much later. It would seem to me to be a shame if we should stop doing research into or thinking about anything which wasnt immediately seen as useful.

[/ QUOTE ]

A number is a reference. I don't see how the definition of an undefined definition can be useful. Maybe try sticking with defined definitions.

Nielsio · #9 07-18-2007, 09:14 PM

But otherwise I agree with you. If this is what interests you, then go for it.

kerowo · #10 07-18-2007, 09:15 PM

If that is the case then no it's not a paradox because the number you have in mind isn't a single number but will change over time as people actually reference it.

If you think about it like a computer does, what you are doing is just giving the address of that number, not the actual number itself. In effect you are never dereferencing that number to get at the actual number itself.