[Falanxi Dacai Shifu], Your Example of All Finite Natural Numbers Is Not the Same as Miss Chan's

Yesterday [Falanxi Dacai Shifu] raised an example about all finite natural numbers. I used "[Falanxi Dacai Shifu], your construction of the example of all finite natural numbers is invalid" to point out the error in his proof, quoted as follows:

"But his proof is incorrect. Let me explain point by point:

Proof by contradiction: Assume the thesis holds -- all finite natural numbers can form a set A.
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The number of elements in this set A is infinite. The proof is simple: if the number of elements in set A were finite, then the largest element N could be found, but N+1 is also a finite natural number, which contradicts all finite natural numbers forming set A. So set A has infinitely many elements.

Construct a number: a1+a2+a3+a4...
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Since the set above is infinite, this number must be in A.

This number is certainly not equal to any number in A, and is also a natural number. Contradiction.
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So you cannot reach this conclusion."

=====Above is the chef's proof; below the lines is my explanation.

Afterward, I further pointed out that Miss Chan's proof differs from the case of all finite natural numbers, quoted as follows:

"Miss Chan's proof is fundamentally different from this. She first uses quantum mechanics and the finiteness of the universe to prove set A is finite. Then the proposition she constructs also satisfies the finiteness requirement but is not in set A. So understanding Miss Chan's proof does require some effort."

But this chef apparently still hasn't understood where the difference lies. So let me patiently explain once more: the reason all human thoughts differ from the situation of all finite natural numbers is that among all finite natural numbers, there is no possible way to prove that the set of all finite natural numbers has finitely many elements. In mathematical theory, it can be proven to be infinite. But the set of all human thoughts has finitely many elements. This point does not depend on a purely mathematical proof -- please everyone take note. This is because humans and natural numbers are different. Humans live in physical space, while natural numbers exist only in a purely mathematical space. Because humans live in physical space, they are necessarily subject to the constraints of physical laws. Miss Chan proved that the set of all human thoughts has finitely many elements precisely from the physical properties that distinguish humans from natural numbers -- because the lifespan of the universe in which humans live is finite, and according to quantum mechanics, the interval at which humans produce thoughts cannot be infinitely short.

Those who oppose Miss Chan's proof all make the same mistake: they don't know that the examination of human thought must be conducted simultaneously in mathematical and physical space. Humans are real humans, not abstract symbols. So using the example of all finite natural numbers to refute Miss Chan is obviously barking up the wrong tree, and also reflects the metaphysical aspect of the opponents' thinking.