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?".

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)?

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)

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.

Originally posted by doodinthemood 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.

Proof by contradiction.

If 7 is an infinite number, than no one could read this thread in his lifetime - Thread 91427. Hence, 7 is finite.