What is the smallest even number?
In an integer, the number divisible by 2 is called even number, also called even number. Even numbers include positive even numbers, negative even numbers and 0. All integers are either odd or even. When n is an integer, even numbers can be expressed as 2n(n is an integer); Odd numbers can be expressed as 2n 1 (or 2n- 1).
In decimal system, we can judge whether the number is odd or even by looking at the single digits: 1, 3, 5, 7 and 9 are odd; Numbers with digits 0, 2, 4, 6 and 8 are even numbers.
0 is a special even number (in 2002, the International Mathematical Association stipulated that 0 is an even number; China also stipulated in 2004 that zero is an even number). It is not only the dividing line between positive even numbers and negative even numbers, but also the watershed between positive odd numbers and negative odd numbers.
If the elementary school stipulates that 0 is the smallest even number, but your junior middle school is negative, when there is a negative even number, 0 is not the smallest even number.
Most teachers think that the smallest even number should be 2, not 0. One of the teachers insisted that the smallest even number should be 0. His opinions are as follows: as long as it contains a number of about 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, it is clearly pointed out in the tenth volume of Mathematics, a textbook for six-year primary schools with nine-year compulsory education: Note: Because 0 can also be divisible by 2, 0 is also an even number. So the smallest even number should be 0.
Most teachers are speechless when they see the textbooks, but they always disagree. Some teachers also pointed out that the last paragraph of the textbook was also clearly indicated. Note: For convenience, when we learn divisors and multiples in the future, the numbers we refer to 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. Personally, I think 0 is a special number, so the textbook clearly points out that 0 is not included in the study of divisor and multiple. Of course, even numbers are extensions of divisors and multiples and should not include 0. So people feel that the textbooks are inconsistent. As mentioned earlier, when studying the divisibility of numbers, it does not include 0; 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, what is the smallest number that can be divisible by both 6 and 9? Most people think it is the least common multiple of 6 and 9, and the result is "18". However, there is another view that the problem is to find the minimum number divisible by 6 and 9, because 0 can be divisible by both 6 and 9, so the result should be 0. It is of little significance to examine 0 on this issue. However, if 0 is the smallest even number, then the smallest number divisible by both 6 and 9 is 0, which is normal.
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. Personally, there is 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. Then 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 are not mixed in the same category. If 0 is an even number, then 0 is very different from other even numbers. Based on the above three points, I also think that it is far-fetched to stipulate that 0 is an even number.
Therefore, personally, it is not appropriate to designate 0 as an even number in primary school mathematics, and the special position of 0 in divisibility should be clarified to avoid some unnecessary disputes.