Infinitesimal is signed, that is, O. Since infinity does not need to be compared with other quantities, it only needs a complete infinity. But not infinitesimal. When it comes to infinitesimal, there must be comparison (a single infinitesimal is actually the number 0), so o(f(x)) is usually used to represent higher-order infinitesimal than f(x).

Infinitesimal is a concept in mathematical analysis. In classical calculus or mathematical analysis, infinitesimal usually appears in the form of functions and sequences. Infinitesimal is a variable whose limit is the number 0, which is infinitely close to 0.

Specifically, when the independent variable x is infinitely close to x0 (or the absolute value of x is infinitely increased), the function value f(x) is infinitely close to 0, that is, f(x)→0 (or f(x)=0), then f(x) is called the infinitesimal amount when x→x0 (or x→∞). In particular, we should not confuse very small numbers with infinitesimal numbers.

Extended data:

Infinitesimal property

1, infinitesimal is not a number, but a variable.

2. Zero can be used as the only constant of infinitesimal quantity.

3. Infinitely small quantities are related to the trend of independent variables.

4. The sum of finite infinitesimals is still infinitesimal.

5. The product of finite infinitesimals is still infinitesimal.

6. The product of bounded function and infinitesimal is infinitesimal.

7. Especially the product of a constant and an infinitesimal is also an infinitesimal.

8. The reciprocal of infinitesimal with non-zero constant is infinity, and the reciprocal of infinity is infinitesimal.

References:

Baidu encyclopedia-infinitesimal