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In the concept of limit, the independent variable x approaches the finite value z arbitrarily. What does random approximation mean?
1, if it's just an ordinary formula with no denominator of 0, it's arbitrarily close.

In other words, x can take an infinite number equal to z, because nothing will happen when the denominator is infinite.

Infinitely approaching z means directly substituting z into the calculation.

2. If the denominator is 0, then any approximation means that you can only approach z arbitrarily.

But you can't take z, because once you take z, the denominator is 0. Regardless of the level of mathematics,

Denominators cannot be 0.

3. The 0/0 limit in advanced mathematics is called infinitive, and there are seven types of infinitive.

No matter what type of infinitive, it can be converted into 0/0 type in the end. Source of all derived formulas

Are the result of 0/0 infinitive. 0/0 type, but both numerator and denominator approach to.

A ratio in the process of 0, rather than the denominator, can really be 0.

4. Because the limit considers a trend, that is, the trend, gentleness, going,,,

So it is a process quantity, and taking the limit is a process. Any of the methods mentioned above is

Refers to constantly taking values, and getting closer and closer to Z every time. This process is constantly going on, without

Go on endlessly.

5, this endless process, we really don't need to put into calculation one by one, this only

It is the thinking method and the calculation method of limit that let us skip it and get the result directly.

The result is that the ratio is constantly updated and getting closer to z, which is inferred in the process.

Ratio trend, this trend is the limit value.

6. Limit theory also existed in ancient China, but we are in the same strain as sophistry.

Today, many math teachers still regard sophistry as a paradox and criticize sophistry all the time.

study However, the western modern mathematical theory has developed the limit theory in sophistry.

Then the theory of calculus was developed. Limit is a watershed, elementary mathematics here and elementary mathematics there.

Advanced mathematics. The last bridgehead of elementary mathematics is analytic geometry, and advanced mathematics comes first.

Bridgehead is a derivative. If you learn the limit well, it will be easy to derive and integrate.

After studying calculus, we, in turn, continue to study analytic geometry, the most obvious example.

One child is calculus combined with vector algebra, which is called vector analysis = vector analysis.

The first topic of applying vector analysis to science and engineering students is electromagnetic field theory.

Come on! Our traditional mathematics is comparable to the west, and the backwardness begins with limit theory!

We have not escaped from the cage of sophistry, we have fallen behind, more and more behind the edge of modern mathematics,

So far, it is still in a marginal position. Our generation has no hope, but it has not made great progress.

A lot of new pedantry. Hope is in you!