Infinitesimal in limit problems of higher numbers In the limit of higher numbers, the definition of infinitesimal is f (x) when x approaches to x0 or when the limit is zero, then f (x) is called the infinitesimal of X in this process. However, in the related proof later, it seems that the definition of infinitesimal when x approaches to x0 appears again. By definition, isn't infinitesimal only a function? Why can it be replaced by a specific symbol (constant?)? Thank you~

Infinitesimal in limit problems of higher numbers In the limit of higher numbers, the definition of infinitesimal is f (x) when x approaches to x0 or when the limit is zero, then f (x) is called the infinitesimal of X in this process. However, in the related proof later, it seems that the definition of infinitesimal when x approaches to x0 appears again. By definition, isn't infinitesimal only a function? Why can it be replaced by a specific symbol (constant?)? Thank you~

When x approaches to x0 or infinity, the limit of F (x) is zero, then f (x) is the infinitesimal of X in this process, and infinitesimal is a function. Sometimes, in order to write simply or to highlight the main part of the function, infinitesimal is represented by special agreed symbols, such as ε, α, β, O, etc. note that these ε, α, β, O, etc. are not constants, but functions of X, only x is omitted

In higher mathematics, the limit is infinitesimal. Does the limit exist?

Existence

What's the difference between the limit of a function at a certain point being zero and the limit being infinitesimal
I sweat, the first floor, I said infinitesimal is infinitesimal, is a special function limit value, not what you mean. The one you're talking about is not infinitesimal, but negative infinity.
Negative infinity, positive infinity and infinitesimal infinity are two concepts.

Infinitesimal is not a specific quantity, the limit is infinitesimal. I have never heard of this saying. Infinitesimal means that infinity tends to 0. Since infinity tends to 0, the limit of function is 0, not infinitesimal