About "zero"

0 is a magic number. Here we will briefly introduce some features and Properties of 0.

The nature of 0:

* Whether 0 belongs to a natural number is still controversial. In the field of number theory, 0 does not belong to a natural number, while in the field of set theory and computer science, 0 belongs to a natural number. In ISO 31-11: 1992, the theory of set stipulates that the natural numbers represented by symbol N include positive integers and 0. China's National Standard GB 3102-1993 makes the same provision with reference to international standards.

* 0 indicates the number of shards.

* 0 is a Gaussian Integer (the Gaussian Integer is the real part (real part) and the virtual part (Virtual part) are the complex numbers of integers ).

* 0 is an even number.

* 0 is non-positive and non-negative. The opposite number and absolute value of 0 are both of them.

* 0 multiplied by any real number is equal to 0 (0*10 = 0), and any real number plus 0 is equal to itself (x + 0 = X ).

* 0 has no reciprocal or negative reciprocal. it is meaningless to divide any number (including 0) by 0.

* 0 cannot be used as the base of the logarithm.

* The Power of Positive numbers of 0 is equal to 0, and the power of negative numbers is meaningless (because the denominator cannot be 0 ).

* 0 to the power of 0 mathematicians have not yet been formally defined. In some fields, such as composite mathematics, the common practice is to define it as 1.

* 0! Defined as 1.

* The maximum approximate number of 0 and any integer is another integer.

* 0 is a multiple of any integer.

 

Several points:

1. dividing any number (including 0) by 0 is meaningless:

Proof: (reverse verification)

If the value of a non-zero real number is divided by 0, there is a non-zero real number X, and there is a = x/0.

In this case, x = A * 0 = 0, which is in conflict with the non-zero X of the question, resulting in a hypothetical error.

Therefore, dividing any non-zero real number by 0 is meaningless.

So why is it meaningless to divide 0 by 0?

First, I would like to explain the significance of dividing 0 by 0 in real life:

For example, if there is 0 yuan, how much money should each person be allocated to 0 yuan now?

When we raise this question, we do not mean that the question has a paradox, but that it is meaningless. In philosophy, 0 people get 0 yuan in total, so each person can get any value. Why? Because the event described in this problem is an impossible event, it will be infinitely possible if an impossible event occurs.

This concept can be combined with Shannon's information theory. Shannon believes that the amount of information carried by a code element is-log (PI), where Pi is the probability that the code element appears. According to this formula, the smaller the Pi, the larger the amount of information. When the PI is 0, the amount of information carried is infinite. That is to say, such an event brings infinite possibilities, it may be a cosmic explosion. Since everything that has been deemed impossible has happened, what else will not happen? Therefore, if 0 people score 0 yuan, each person may receive any value.

Then, I will explain some mathematical concepts:

In the limit theory, if any non-zero real number is divided by 0, the result is infinite (possibly positive infinity or negative infinity ).

For 0/0, the value of limit theory may be any value.

For example, the 0/0 rule of law:

In the law of lobida,

Set the f (x) and g (x) functions to meet the following requirements:

WhenX => Oo, Lim f (x) = lim g (x) = 0; At the same timeF (x)AndG (x)Can be exported.

Then, there will beLim (f (x)/g (x) = Lim (f' (X)/G' (x) =.

From this, we can see that f' (X) and G' (x) have multiple possibilities due to the various possibilities of Functions f (x) and g (x, result A may also have multiple possibilities.

That is, the result of 0/0 can be any value, which is meaningless.

2. Zero is a Gaussian Integer:

The Gaussian Integer is the real part (real part) and the virtual part (Virtual part) are the complex numbers of integers.

Proof:

Set 0 = a + B * j, with a = B = 0. Since 0 is an integer, it is defined as a Gaussian Integer.

3. Zero is a multiple of any integer:

Proof:

If any integer is set to

For any non-zero integer a, there are 0/a = 0. Since 0 is an integer, 0 is a multiple of.

In the case where a is 0, 0/0 mentioned above is meaningless, so you do not have to consider it.

4. The maximum common divisor of zero and any number is another number:

Since there is a previous rule: 0 is a multiple of any integer.

Therefore, for a and 0, 0 is a multiple of A. Therefore, the maximum common divisor of A and 0 is naturally.

 

0

1. Zero effect: placeholder

For example, in decimal format 1024, where 0 plays a role? 0 of 1024 indicates that the hundred bits are "NONE ". Although not, this 0 cannot be omitted, because if 0 is omitted and written as 124, it becomes another number.

In the count by bit method, digits are of great significance. Even if the hundreds of digits are "NONE", you cannot write a number. Then it is the turn of 0, that is, 0 is used as a placeholder. In other words, 0 occupies a position to ensure that digits above it do not produce misplacement.

Because there is a 0 indicating "NONE", the value can be correctly displayed. It can be said that 0 is indispensable in the count by bit method.

2. Effect of zero: "no"

We need to use a number to indicate "NONE" and "no ". 0 in its definition is "NONE" and "NONE ".

On the one hand, 0 represents a state of material existence in the natural world-None. This state is meaningless, but as a supplement to "yes", it represents the general law of the natural world: whether or not there is mutual occurrence.

On the other hand, it is the "NONE" State represented by 0, which can well describe the "NONE" We have come into contact ", let "no" exist in the "yes" World in the "0" way.

 

0 in daily life

In our daily life, sometimes there is a situation where 0 represents "none.

* No plan

We often use calendars to manage plans. Fill in the "desk work", "business trip", "Seminar" and other plans in the calendar. So what is the equivalent plan of "0?

Generally, if we don't have any schedule for the "Seminar" mentioned above on a certain day, all the time is at our discretion, so now we are in an unarranged situation. In this case, we can use 0 to indicate that there is no arrangement or plan. 0 is equivalent to an empty plan, and there is no arrangement in the schedule, it is empty, that is, 0.

Here, 0 plays a role as a placeholder.

* Drugs without Efficacy

Assume that a certain capsule must be regularly taken once every four days, that is, three days, and one day. However, it is very difficult to cycle such a period.

The magic of action comes naturally. That is, take medicine every day. However, each four capsules contains a fake capsule that has no efficacy. Is it better to prepare a box with a date in advance and put the medicine to be taken every day?

In this way, you do not need to determine whether the "Today is the medication day or the withdrawal Day. Because there is no effective medicine, it forms a simple rule of taking a capsule every day. Here, 0 still serves as a placeholder.

About "zero"