Actually I'm not assuming that the produced number has a finite amount of non-zero digits (since it may have an infinite amount of leading zeros and still be an integer)
But anyway I've been convinced. Thanks to everyone for your answers
matt, not to mean disrespect but I believe saying "it's so because it is" is not very illuminating, at least if you're trying to be didactic (as opposed to viewing this as a confrontation or who-knows-more contest). You of course don't have to prove that I'm wrong, but since you take the...
Yes, but I have trouble seeing that the diagonal argument applied to integers implies an integer with an infinite number of digits. I mean, intuitively it may seem obvious that this is the case, but then again it's also obvious that for every integer n there's another integer n+1, and yet this...
Well, the typical set of reals in which you flip a digit (of their decimal representation) each time, producing a new real.
Ok, let's say I have the list of integers. For each integer, I pick a random digit position (different from the ones picked previously), zero-padding if necessary and...
An example of the original argument? yes of course. But the problem is that seemingly I can apply the same reasoning to just the integers to get a contradictory result and I don't see where the fault is...
Hi
I've some trouble understanding (or maybe accepting) Cantor's diagonal argument. When I was young I had no trouble accepting it and it seemed perfectly logical, but after a long hiatus and returning to my original interests, I seem less than convinced (must be some age-related or brain decay...