# Is 7 a finite numbr?

FabianFnas
Posers and Puzzles 16 Apr '08 12:27
1. 16 Apr '08 12:27
In a book about number and infinity I found this question:
"Can you prove, without circularity, that seven is a finite number?"

Of course 7 is a finit number, it is just - 7, what else? And I know for sure that it is not infinite, then it must be finite, doesn't it?

But strictly, if anyone claims that 7 is in fact finite, than he must be able prove it, or he just have to asume it.

After a day or two (or if you want to discuss it further than that) I'll present the book's answer.
2. 16 Apr '08 12:36
Originally posted by FabianFnas
In a book about number and infinity I found this question:
"Can you prove, without circularity, that seven is a finite number?"

Of course 7 is a finit number, it is just - 7, what else? And I know for sure that it is not infinite, then it must be finite, doesn't it?

But strictly, if anyone claims that 7 is in fact finite, than he must be able prove ...[text shortened]... day or two (or if you want to discuss it further than that) I'll present the book's answer.
I think the first thing I'd ask is "how are you defining a finite number?".
3. 16 Apr '08 12:36
Originally posted by FabianFnas
In a book about number and infinity I found this question:
"Can you prove, without circularity, that seven is a finite number?"

Of course 7 is a finit number, it is just - 7, what else? And I know for sure that it is not infinite, then it must be finite, doesn't it?

But strictly, if anyone claims that 7 is in fact finite, than he must be able prove ...[text shortened]... day or two (or if you want to discuss it further than that) I'll present the book's answer.
Can you define a "finite number"? Are you meaning, essentially, a "finite cardinality" - where a "cardinal" is a number used to denote the size of a set (of objects/numbers/whatever)?
4. 16 Apr '08 12:371 edit
Originally posted by mtthw
I think the first thing I'd ask is "how are you defining a finite number?".
oooh-you're fast!
5. 16 Apr '08 12:38
Originally posted by Swlabr
Fastard!?
6. 16 Apr '08 12:52
Fastard!?
not your fast - his fast.
7. 16 Apr '08 13:44
Originally posted by Swlabr
not your fast - his fast.
Just being facetious.
8. sonhouse
Fast and Curious
16 Apr '08 13:51
Just being facetious.
or fast tidious.
9. 16 Apr '08 14:11
Originally posted by sonhouse
or fast tidious.
10. 16 Apr '08 14:16
We are somewhat off-topic now, are we not...?
11. 16 Apr '08 16:16
Define numbers.
12. eldragonfly
leperchaun messiah
16 Apr '08 17:22
What matthw said.
13. 16 Apr '08 18:302 edits

A set S is inifite if there exists a proper subset S' whose elements can be put into 1-to-1 corresponence with S ( there is a bijection from S' to S ).

Hence a set S is finite if no proper subset S' can be put into 1-to-1 correspondence with S. Then the cardinality of S is an finite integer.

Finally a number n is finite if there exists a finite set S whose cardinality c is such that Abs(n) < Abs(c)
14. 16 Apr '08 19:23
Suppose 7 is infinite, then the title of this thread would contain an infinite number, but redhotpawn.com does not allow titles that are infinitely long. Thus, 7 is finite.