When marking an exam, there was a question on the fifth grade paper: What is the smallest even number? Most teachers think it is 2, but one teacher thinks it is 0. A stone stirs up a thousand waves, causing heated discussion.

What is the smallest even number?

Most teachers think that the smallest even number should be 2, not 0. One of them insisted that the smallest even number should be 0. Her opinions are as follows: as long as it contains a number around 2, it is an even number; As long as it is a multiple of 2, it is an even number. Because 0÷2=0, 2 is a divisor of 0 and 0 is a multiple of 2. The textbook stipulates that the number divisible by 2 is called even number, so the smallest even number should be 0. In particular, page 53 of Mathematics, a textbook for nine-year compulsory education and six-year primary schools, clearly points out: Note: 0 can also be divisible by 2.

Most teachers are speechless when reading textbooks, but they always disagree. Some teachers also suggested that the last paragraph on page 49 of the textbook should also clearly state, note: for convenience, when learning divisors and multiples in the future, the numbers we say generally refer to natural numbers, excluding 0.

Is the smallest even number 0 or 2? Although the textbook clearly points out that 0 is an even number, it never explicitly points out that the smallest even number is 0. The author thinks that 0 is a special number, so the textbook clearly points out that it does not include 0 when learning divisor and multiple. Of course, even numbers are extensions of divisors and multiples and should not include 0. So it makes me feel that the textbook is inconsistent. As mentioned above, when studying the divisibility of numbers, 0 is not included; But when it comes to the concept of even number, it is clearly pointed out that 0 is also an even number.

If 0 is the smallest even number, then many questions become meaningless. For example, (1) "What is the smallest number divisible by both 6 and 9?" Most people think it is the least common multiple of 6 and 9, and the result is "18". But another point of view is that the problem is to find the minimum number divisible by 6 and 9, because 0 can be divisible by 6 and 9, so the result should be 0. It is of little significance to investigate 0. But if 0 is the smallest even number, it can be divisible by 6 and 9.

0 is the smallest even number, so after a negative number appears in junior high school, is 0 still the smallest even number? When negative numbers appear, the smallest even number does not exist, just as the largest natural number cannot be found. The author has an understanding that the textbook stipulates that 0 is an even number, and this property is also debatable. Because 0 can also be divisible by 2, 0 is even. So 0 can also be divisible by any natural number. What is 0? As we know, a feature is necessarily different from other things; A feature, in the same thing, must also have the same external or internal performance; The essential attributes of things must be mutually exclusive with those of other kinds of things. If they are not mutually exclusive, then they should not be mixed in the same category. As the central leadership recently said: "Where there are black forces, there is definitely not enough red, and red and black cannot be tolerated." If 0 is an even number, then 0 is very different from other even numbers. It is far-fetched to analyze with the above three points.

Therefore, the author thinks that 0 should not be designated as an even number in primary school mathematics, and the special position of 0 in divisibility should be made clear to avoid some unnecessary disputes.

I hope my colleagues will correct me on the above points.