Achilles paradox was put forward by Zhi Nuo, an ancient Greek philosopher in the 5th century BC. The content is to let the tortoise start in front of Achilles 1000 meters and race with Achilles. Suppose Achilles' speed is 10 times that of the tortoise.
After the start of the race, if Achilles runs 1000m, assuming that T is needed, the tortoise will lead him1000 m.. When Achilles finished the next 100 meters, his time was t/ 10, and the tortoise was still ahead of him 10 meters. Achilles ran the next 10 meter, using his t/ 100 meter, and the tortoise was still ahead of him 1 meter.
There are different definitions of infinity in set theory. German mathematician Cantor proposed that the number of elements (cardinality) corresponding to different infinite sets has different "infinity". The sum of two infinite quantities is not necessarily infinite, the product of bounded quantity and infinite quantity is not necessarily infinite (for example, the constant 0 is a bounded function), and the product of finite infinite quantities must be infinite.
There are different definitions of infinity in set theory. German mathematician Cantor proposed that the number cardinality of elements in different infinite sets corresponds to different "infinity". The only way to compare different infinite "sizes" here is to judge whether a one-to-one correspondence can be established and abandon Euclid's view that the whole is greater than its parts.
The essence of infinity:
1, the sum of two infinite quantities is not necessarily infinite.
2. The product of bounded quantity and infinite quantity is not necessarily infinite (for example, a constant of 0 is a bounded function).
3. The product of finite infinity must be infinite.
4. In addition, the fact that a series is not infinite does not mean that it is bounded (for example, series 1,1/2,3, 1/3, ...).