1, Russell paradox
Cantor's set theory is the most revolutionary theory in the history of mathematics, and its development path is naturally uneven. It was not until the death of the overbearing clone Nick (a professor at the University of Berlin, who was very influential and completely denied the set theory) that the set theory had its day, but it didn't last long, because the appearance of Russell's paradox directly impacted the two disciplines that have always been considered rigorous, thus shaking the foundation of mathematics.
2. Zeno paradox
Zhi Nuo is a representative of Elijah School in ancient Greece. He put forward four famous paradoxes, the most important of which is Achilles' paradox of chasing turtles, that is, the fastest Achilles can never catch up with the slowest turtle, that is, V & gtVq, but V is a little ahead. Achilles had to go beyond the tortoise's starting point to catch up with it, but when Achilles reached the tortoise's starting point, the tortoise reached a new point. At this rate, Achilles will never catch up with the tortoise.
3. The liar paradox (semantic paradox)
In the 6th century BC, Epimenendez, a philosopher in Crete, ancient Greece, made the following conclusion: Everything that Cretes said was a lie. ? If it is true, because Epimenendez is also from Crete, the inference is false, but it does not lead to contradictions. After Euclid's improvement, he later became? What I'm saying now is a lie? . If it is true, it is inferred to be false; If it is a lie, then it is introduced as true. Later, people transformed the reinforcement paradox into the paradox of liar:? Is that sentence written on this page false? Because there is nothing in the above line except this sentence itself, if this sentence is true, we must admit its conclusion, then this sentence is false; If the statement is false and the statement is true, it is actually a mixture of the statement as an assertion and the statement as a judgment. Paradox of semantics ".