A Crete said, "I was lying when I said this." Then the Crete asked the audience if what he said above was true or not. This paradox comes from Epimendez, Crete, Greece in the 6th century BC, which makes the Greeks nervous. Even the Western Bible, the New Testament, quoted this paradox.

For Crete, "I lied when I said this" can neither tell the truth nor the truth.

2\ Plato and Socrates Paradox

Plato teased his teacher: "What mr. socrates said below is a lie."

Socrates replied, "Plato's words are right."

Whether Socrates' words are assumed to be true or false, it will cause contradictions.

3\ The paradox of eggs

Chicken or egg first?

4\ Paradox of book title

Miao Ling, an American mathematician, wrote a book entitled "What is the title of this book?" He asked: What is the title of Miao Ling's book?

5\ Father-daughter Paradox in India

The daughter wrote on the card: "You have to write a' no' on this card before 3 o'clock this afternoon." Then the daughter asked her father to judge whether what she wrote on the card would happen; If the judgment will happen, write "Yes" on the card, otherwise write "No". Q: Does father write "yes" or "no"?

6\ Worm paradox

A bug crawls from one end to the other at a speed of 1 cm per second, and the rubber rope extends in the same direction at the same time at a speed of 1 m per second. Do bugs crawl to the other end? Every time the worm advances 1 cm, at the same time, the other end of the rope is pulled away 1 m, which is too close to reach the sparse, and I am afraid it will never climb to the end.

Now let's see:

Within 1 sec, the worm climbed to1100 of the rope (meaning100, the same below).

In the second, the bug climbed to 1/200 of the rope.

- ,

In the nth second, the bug climbed up to 1/N× 100 of the rope.

In the first 2 seconds to the power of k, the ratio of the total crawling distance of the worm to the total length of the rope is

1100 (1+1/2+1/3+-+1/2 to the k power)

but

1+1/2+1/3+-+1/2 to the k power.

=( 1+ 1/2)+( 1/3+ 1/4)+( 1/5+ 1/6+ 1/7+ 1/8)+ -

+(65438th power of k-1+0/< 2+1 > k power of+1+2 >+-+ 1/2) > 65443.100.

———————————∨————————

* * * K- 1 power term with 2

= 1+ 1/2+ 1/2+-+ 1/2 = 1+K/2

———∨—————

The k power term of * * * is 2.

When K= 198, 1+K/2= 100, so1100 (1+1/2+/kloc-

So in 2 198 seconds, the bug climbed to the other end of the rope.

This paradox is caused by intuition. (Note: I don't have a tool to write mathematical symbols, so the "/"here refers to a semicolon, and the k power of 2 refers to the k power of 2, for example, the 3 rd power of 2 is 2 and the 3 rd power of 2 equals 8)

7\ Paradox of Tortoise and Rabbit Race

The tortoise said to the rabbit, "You can't catch up with me. I'm in front of you now 1 m. Although your speed is 0/00 times of mine, when you catch up with my present position, I climbed 1 cm to C 1 point. By the time you got to C 1, I had climbed from you to 1/. Of course the rabbit refuses to accept it, but it can't beat the tortoise. In fact, the race took less than 1 second, and the rabbit had already run in front of the tortoise.

Readers are invited to defend rabbits. (Similar to the above calculation)

8\ language paradox

N is the smallest positive integer that cannot be defined by more than 25 natural words.

There are only 23 natural words in the above definition of n, but no more than 25, that is, n is defined with no more than 25 natural words, which contradicts that n cannot be defined with no more than 25 natural words.

The reason for this paradox is that there is no strict standard on how to determine the number of words defined by natural words, and what is "undefined" is also ambiguous.

9\ Election Paradox

In the elections of A, B and C, opinion polls show that two-thirds of voters prefer A to B, and two-thirds prefer B to C. So A said, "According to protecting two-thirds of voters who oppose B and two-thirds of voters who oppose B, it shows that I am better than B and B than C, so I am better than C, so I am the best and should choose me." C refused, saying, "Protect A against B 1/3 voters against A, protect C, protect B against C 1/3 voters against A, protect C, thus forming two-thirds voters who protect C and oppose A. According to your logic, I am also superior to you, you are superior to B, and I am the best. B went on to say, "According to you, B is better than C, and C is better than A, so B is better than A, that is, I am also the best, so I should be chosen. "

What can this poll show?

This paradox originated from kenneth j. arrow, who won the Nobel Prize in Economics in 1972. 195 1 He gave the election axiom of so-called democratic election, in order to make the election fair and reasonable and avoid the odious problem of dictator manipulating the election. Later, he proved a theorem that there is no perfect democratic election that satisfies Arrow's axiom.

10\ Baldness paradox

An old bald professor argued with his students about whether he was bald or not.

Professor: Am I bald?

Student: You don't have much hair. I should say yes.

Professor: Your hair is very dense. You are definitely not bald. Let me ask you, if you lose a hair on your head, can you say you are bald?

Student: Of course I won't go bald without losing a hair.

Professor: Well, after summing up our discussion, we have come to the following proposition:' If a person is not bald, then he is still not bald if he loses a hair', right?

Student: Yes!

Professor: When I was young, I was as beautiful as you. Nobody said I was bald at that time. Later, with the growth of age, the hair was reduced to what it is today. But every time I lose a hair, according to our proposition just now, I should not be called baldness, so after a limited number of haircuts, the conclusion is:' I am still bald today'.