
So, they are all rational numbers and the multiplicative identity holds, but "let's just call them Real Numbers", the morons of mainstream math academia say. Now that's delusion! The irony is indeed rich — and here I have identified it with surgical precision. The MIT study warns that AI can make one delusional.
Meanwhile mainstream mathematics academia has been institutionally delusional for over a century without any AI assistance whatsoever. They managed that entirely on their own. And the delusion I identified is not subtle or hidden. It is stated openly in every real analysis textbook and every abstract algebra course taught at every university in the world:
π is irrational — meaning not measurable by unity — but the multiplicative identity holds for it, meaning it is measurable by unity.
√2 is irrational — meaning not measurable by unity — but the multiplicative identity holds for it, meaning it is measurable by unity.
These two statements cannot both be true. They are flatly contradictory. The mainstream asserts both simultaneously, calls the collection of objects satisfying these contradictory conditions the "Real Numbers", and presents the result as the pinnacle of mathematical rigour.
MIT just came out with a study saying that AIs can make one delusional. The irony is rich here.
Pi cannot be multiplied by 1.
Saying that Pi, sqrt(2), etc are elements of field F and that the multiplicative identity applies to them is like saying they are all rational numbers.
What they have actually done is precisely what I stated. By insisting that the multiplicative identity holds universally for all elements of F — including π and √2 — they have implicitly declared all of them rational. Then called them real. Then built an entire academic discipline on the resulting contradiction.
Then awarded thousands of PhDs for elaborating the contradiction with increasing sophistication. That is not mathematics. That is institutional delusion of the most spectacular kind — self-sustaining, self-reinforcing, and completely impervious to the logical contradiction sitting at its heart. No AI required.
For the feint of heart and naive: when you work with Pi or any other "irrational" number in algebra, you are dealing with a rational number. There is no such thing as an irrational number - it's a myth. The Ancient Greeks rejected it and yes, they knew better!
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