Thread: Justification for believing in a maximum finite number

I watched this program the other day BBC iPlayer - Horizon: 2009-2010: To Infinity and Beyond and while I didn't like most of it, I was intrigued with what Doron Zeilberger had to say (21 minutes 30 seconds into the video). He said that there is no such thing as infinity and that it has no place in mathematics, which on it's own is a reasonable statement, but then actually asserts that there is a finite number that is the largest number that is logically possible to have in mathematics, and then makes the even weirder statement that once you have found that number, adding 1 to it would bring you back to 0. I don't want to know whether anyone thinks that this is right or not, I'd just like to know what could have led Zeilberger to the conclusion that there is a "largest" finite number which it is impossible to go higher than. A search on google didn't find me anything other than links to his research papers which I'm sure I'm not educated enough to understand, so if anyone knows of any form of possible justification for holding this belief then it would be greatly appreciated if you could tell me

Thanks in advance for any replies.

Originally Posted by Freddie69

I watched this program the other day BBC iPlayer - Horizon: 2009-2010: To Infinity and Beyond and while I didn't like most of it, I was intrigued with what Doron Zeilberger had to say (21 minutes 30 seconds into the video). He said that there is no such thing as infinity and that it has no place in mathematics, which on it's own is a reasonable statement, but then actually asserts that there is a finite number that is the largest number that is logically possible to have in mathematics, and then makes the even weirder statement that once you have found that number, adding 1 to it would bring you back to 0. I don't want to know whether anyone thinks that this is right or not, I'd just like to know what could have led Zeilberger to the conclusion that there is a "largest" finite number which it is impossible to go higher than. A search on google didn't find me anything other than links to his research papers which I'm sure I'm not educated enough to understand, so if anyone knows of any form of possible justification for holding this belief then it would be greatly appreciated if you could tell me

As an underrate I majored in both mathematics and philosophy. My favorite philosophy professor would taunt some of us by saying "infinity is where mathematician hides his ignorance".

But in this case I know that Zeilberger means the there is no one magnitude of the infinity.
The idea is really simple: given any set, the set of all of its subsets is a larger set.
So there can be no largest collection.

Thank you very much for your reply. If that's what Zeilberger means then OK I can understand that, but that's not what he was trying to say as far as I can tell. What point was he trying to make by saying that if you add one to the largest number (and to me it seemed that he'd was saying that there actually is a defined number than we can't get larger than) then it will bring you back to zero?