Recent content by AlienRenders

The infinite identity matrix is basically the diagonal in Cantor's proof. You can represent it as a grid of 0's with 1's along the diagonal. Let f(n) be a row/element. d(n) of f(n) is 1. Everything else is 0.I'm not aware of any other definition for "proper subset". It's where all elements of...

Does there not exist a set S ⊂ L where each element s of S is defined as a string of 0's except for d(n) = 1. The range is a subset of L, yet the domain n is the same. That's a big problem, no?

Remapping and catenation is all fine outside of Cantor's diagonal. Enumerating Q for example is an interesting technique. But is the infinite identity matrix not a proper subset of my list if I write N binary strings and compare by digits? Is there not a 1 in each possible position n in this...

I'm happy to continue this in private if possible. I want to respect the mods decision.

How many rows in my list match a row in the infinite identity matrix when comparing digit by digit? Are there not infinitely many? Yet it is not my entire list N which consists of only strings in base 2. How can this be if there is a bijection between the rows and digits of my list? Just...

@stevendaryl You're again using the same variable n to index into two sets that don't have a bijection. You're just avoiding the issue now.

@stevendaryl You're ignoring what I'm saying and throwing insults. I'll ask my same question again. How many rows in my list match a row in the infinite identity matrix when comparing digit by digit? That's all of the rows from the identity matrix. There are infinitely many of them. They are...

Let me ask you this. How many rows in my list match a row in the infinite identity matrix when comparing digit by digit? Yet, this is not my entire list.

You know very well what digits and rows. The diagonal uses it for goodness' sake. Please stop this nonsense. When you ASSUME that there are as many real numbers as there are digits in a single real number, this isn't true for N either. It's a given that it isn't true. If it's not true for N...

Fair enough. I was just looking for the proof that the digits and rows were one to one. If that proof doesn't exist, then so be it. I'm satisfied that Cantor's proof is incomplete.

So because you get completely destroyed in your arguments, you resort to appeals to authority?

Of course it does. You are grabbing a digit x from a row y. The digits and rows are two different sets. My apologies for not adding g(n, x) and h(n, y). These sets are not one to one. Please stop the trite aggressive statements please. They don't help. You didn't add a function either. So there...

That wasn't my term. I never said something was not countably infinity. Nice of you to jump in so aggressively though.

@FactChecker That's an extremely weak argument. The rows and digits are not one to one. You must prove that they are before Cantor's diagonal proof can work. Countably infinite is not enough otherwise you could prove that |N in base 2| < |N in base 3| by showing that there are numbers in base 3...

It's simple. If there exists a row from the identity matrix for each digit and all other rows of N can be constructed from combining these rows (binary OR operation), then there are no more digits remaining to construct the diagonal for the rest of my list. End of story. The assumption that the...