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.
Originally posted by FabianFnasI think the first thing I'd ask is "how are you defining a finite number?".
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.
Originally posted by FabianFnasCan 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)?
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.
how about this:
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)
Originally posted by doodinthemoodIf 7 is an infinite number, than no one could read this thread in his lifetime - Thread 91427. Hence, 7 is finite.
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.
Also proof by contradiction.