Let Me Explain Infinity and Finiteness to Mathematics on Miss Chan's Behalf

The forum user Mathematics posted:

"Now Miss Chan constructs a thought: U (this thought is different from any of the thoughts an, but she hasn't expressed this clearly. Since U is logical conjunction, what are the objects being conjoined? Is it the entirety of my one hundred thoughts? Fine, let's continue. Then, the thought produced by U, since it is formed by conjoining my 100 thoughts, is therefore also finite, and it is also? My thought? A thought different from my previous one hundred thoughts? So Miss Chan declares she has found a contradiction?"

Here Mathematics is again being somewhat dishonest, because Miss Chan's post had a very clear definition: "Then we construct a thought as follows: U (the expression of this thought differs from thought an), where U represents logical conjunction, and an represents all elements of set A." Here the objects being conjoined are "(the expression of this thought differs from thought an)," where "an represents all elements of set A" -- anyone who has studied mathematics knows what this means. But in Mathematics' quotation, parts were intentionally or unintentionally left out, becoming "Miss Chan now constructs a thought: U (this thought is different from any of the thoughts an." Excuse me: is "U (this thought is different from any of the thoughts an" the same thing as "U (the expression of this thought differs from thought an), where U represents logical conjunction, and an represents all elements of set A"?

Because Mathematics fundamentally didn't understand Miss Chan's definition, everything he said was completely off base, having nothing to do with Miss Chan's proof. Here, let me explain Miss Chan's definition. Using the simplest example: set A has two propositional elements: "the sky is blue" and "the sky is not blue." The new thought defined by Miss Chan would be: "The expression of this thought differs from the thought 'the sky is blue' AND the expression of this thought differs from the thought 'the sky is not blue.'" This thought is about expression, and is different from both of the original propositions "the sky is blue" and "the sky is not blue." For any set A containing N elements, the expression above is analogous.

Miss Chan gave a specific thought, and this thought is finite -- that is, it can be expressed using a finite number of symbols. Here let me quote Miss Chan's proof again. Everyone can compare it with the above example -- it involves absolutely no infinity:

Because the leftist hypothesis states that "all linguistically expressible human thoughts can be stored in a binary computer," these thoughts constitute a set A, where thoughts are denoted by an, with n representing natural numbers. Since the universe will perish, and the time interval for humans to produce a thought cannot be infinitely short (otherwise it would violate the principles of quantum mechanics), we can know that the elements in set A are finite, though the quantity can be very large. Then we construct a thought as follows: U (the expression of this thought differs from thought an), where U represents logical conjunction, and an represents all elements of set A. This thought is obviously not in set A, and it cannot be simplified into any thought in A, because this thought speaks of expression, so any tricks of logical simplification are useless. Since set A is finite, the expression of this thought is also finite, and this thought is obviously a human thought. The contradiction can only come from the leftist hypothesis that "all linguistically expressible human thoughts can be stored in a binary computer" -- meaning this hypothesis is absurd."