[Pangguanzhe Ruju], Your Error Is the Same as [Falanxi Dacai Shifu]'s!

[Pangguanzhe Ruju] wrote "Miss Chan, I don't appreciate you showing off in front of me." First of all, Miss Chan seems to write posts for everyone to see. If [Pangguanzhe Ruju] feels that anyone writing a post is doing something at his doorstep, I have no objections. What Miss Chan thinks about it is not my business. But from his post, even if he has a door, it's not one worth "showing off" in front of! Quoted as follows:

"Now let the set of all human thoughts be T, with elements called c. Mathematics' conclusion is that human thoughts can be computer-encoded, that is, there exists an injection f: T --> N."
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This is the same taken-for-granted assumption as the chef's claim that "human thoughts can form a set A. Then following the Chan lady's construction, there exists a human thought not belonging to A." Because all human thoughts can't even form a set -- it's similar to the concept of "the set of all sets" in Russell's paradox. Miss Chan is very clear on this point. Her set involves not all human thoughts, but only computer-recordable human thoughts, which can form a set because this is determined by the computer's mode. According to Miss Chan's construction, set A is not human thoughts in general, but all computer-recorded human thoughts. The constructing agent is a human; the things being constructed are computer-recorded human thoughts. This gentleman can't even get the most basic set concepts straight yet proceeds to prove things -- isn't that a bit inappropriate?

Continuing the quote:
"Actually we can be even more relaxed. We use 1 and 2 instead of 1 and 0. Then an encoding, say 11221, we can write as 0.11221, a number in the interval [0,1]. Even if a thought is infinitely long, 0.111222111222... is still a number in [0,1]. To summarize, what Mathematics needs to prove is: there exists an injection f: T --> [0,1]. Proof: the total of all human thoughts to date is finite, so |T| < |N| < |R| = |[0,1]|. QED."
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This person can't even get the most basic terms of the discussion straight. First, Mathematics requires binary with finite digits. Also, that thoughts can't be infinitely long is already a consensus -- this is determined by the physical properties of our universe. Even that chef understands this, yet this person still doesn't understand at all. Isn't that a bit too inappropriate?

So your injections, surjections, and all that are completely off-target. You don't even understand the most basic consensus already reached. Your entire proof doesn't even match up to the chef's. From the current situation, the chef is actually the most knowledgeable person among them. Of course, his biggest remaining problem is that he still hasn't figured out the difference between the human brain and the computer -- that's what he needs to keep working on. As for this person: first get the issues straight. Miss Chan's proof is not a purely mathematical proof -- it depends on the computer's recording mode and the finiteness of the universe's existence time. Also, Miss Chan's proof has nothing to do with any numbers, let alone functions. Please note: it is not possible to define functions under all circumstances. This is also a word of advice for those who define things arbitrarily!