Cantor Was Wrong | There Are No Infinite Sets
The foundations of modern mathematics are flawed. A logical contradiction is nestled at the very core, and it’s been there for a century.
Of all the controversial ideas I hold, this is the most radical. I disagree with nearly all professional mathematicians, and I think they’ve made an elementary error that most children would discover.
It’s about infinity. I’ve written about infinity here, here, and here, and each article points to the same conclusion:
There are no infinite sets.
Not only do infinite sets not exist, but the very concept is logically contradictory – no different than “square circles”.
Infinite sets are quite literally enshrined into the modern foundations of math – with what’s called “The Axiom of Infinity”. It simply states that, “At least one infinite set exists.” Specifically, the set of natural numbers (1, 2, 3, 4, 5, and so on).
Superficially, it seems like the answer to the question, “How many numbers are there?” is “Infinity!”, but that’s not a precise answer – especially if we do not carefully define our terms.
Mathematical Proof
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