Is it right to say that the limit of infinitesimal is 0?

Is it right to say that the limit of infinitesimal is 0?

To be exact, when the independent variable x is infinitely close to x0 (or the absolute value of x increases infinitely), the function value f (x) is infinitely close to zero, that is, f (x) = 0 (or F (x) = 0), then f (x) is said to be the infinitesimal when x → x0 (or X →∞). For example, f (x) = (x-1) 2 is the infinitesimal when x → 1, f (n) = the infinitesimal when n →∞, F (x) = SiNx is an infinitesimal when x → 0. In particular, we must not confuse a very small number with an infinitesimal
Beginners should pay attention to the fact that infinitesimal is the limit of a function, not the quantity 0. It means that the limit of an independent variable is the quantity 0 under a certain change mode. When a function is called infinitesimal, we must explain the change trend of the independent variable. For example, X ＾ 2-4 is the infinitesimal when x → 2, but we can't generally say that x ＾ 2-4 is infinitesimal
Infinitesimal is usually expressed in small Greek letters, such as α, β, ε, and sometimes α (x), ο (x), etc., which means that infinitesimal is a function of X
Infinitesimal has the following properties:
1. The sum of finite infinitesimal algebras is still infinitesimal
2. The product of finite infinitesimals is still infinitesimal
3. The product of bounded function and infinitesimal is infinitesimal
With the concept of infinitesimal, we will naturally associate with the concept of infinity. What is infinity?
Definition of Infinity: when the independent variable x tends to a, the absolute value of the function increases infinitely, then f (x) is said to be the infinity when x → a
Similarly, infinity is not a concrete number, but a trend of infinite development