Sophisticated people will always come up with a lot of "bases" when demonstrating their truth, so on the surface, they can always confuse some people.

For example, 2=3 is a famous mathematical sophistry, and some people use the following methods to illustrate that this conclusion is correct.

Because 4- 10=9- 15 5

So 4-10+25/4 = 9-15+25/4.

2 squared -2 times 2 times 5/2+(5/2) squared =3 squared -2 times 3 times 5/2+(5/2) squared.

The square of (2-5/2) =3-5/2, and 2-5/2=3-5/2.

So 2=3.

The conclusion of 2=3 is obviously incorrect, but where is the problem?

(Note: A's square -2 times A times b+b's square =(a-b))

The error is from (2- 5/2)2=(3- 5/2)2 to 2- 5/2=3- 5/2.

Obviously 2-5/2 < 0, 3-5/2 > 0,

So 2-5/2 ≠ 3-5/2.

Paradox is that there are two opposite conclusions on the surface of the same proposition or reasoning, and both conclusions can be proved to be justified. The abstract formula of paradox is: If event A occurs, it is deduced that it is not A; if it is not A, it is deduced that it is A. ..

Interesting number paradox

Overview: 1 is a non-zero natural number, 2 is the smallest prime number, 3 is the first odd prime number, 4 is the smallest composite number and so on; If you can't find the interesting feature of this number, it is the first boring number, which is also very interesting.

Therefore, Nathaniel Johnston, a researcher in the field of quantum computing, defined these interesting integers as a whole and arranged them into a sequence, such as prime numbers, Fibonacci numbers, Pythagoras numbers and so on. Based on this definition, Johns proposed in his blog in June 2009 that the first number that did not appear in the sequence was 1 1630. After updating the monthly series of 20 1 1 in 2003, he said that 14228 was the smallest boring number.