The so-called infinitesimal means that the limit is 0. If f(x) is defined in a neighborhood of x0, and lim(x→x0) f(x)=0, it is said that f(x) is an infinitesimal of x→x0. Similarly, infinitesimal is local. Infinity is just a name. For infinitesimal, there is a comparison of infinitesimal.

High-order infinitesimal: If F and G are infinitesimal quantities of x→x0, and lim f/g=0, then F is the high-order infinitesimal quantity of G, which actually accelerates the speed to 0.

Same-order infinitesimal: If F and G are infinitesimal of x→x0, lim f/g=c, and C is non-zero, then F is the same-order infinitesimal of G, that is, the speed of approaching 0 is almost the same (it is the same series). In particular, c= 1 has f, and g is equivalent infinitesimal, which can be replaced in calculation (the speed of approaching 0 is consistent).

Note: 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.