Why is the limit of infinitesimal not negative and 0?

Why is the limit of infinitesimal not negative and 0?

Infinitesimal means that although it is too small for us to distinguish, it does exist. Therefore, it should be a number greater than 0. At most, it is too small to be zero. Negative numbers are not only absent, but also insufficient

Is the result of limit 1 / infinitesimal 0?

Because nonzero infinitesimal and infinitesimal are reciprocal, 1 divided by infinitesimal equals 1 times infinity = infinity

Using the property of infinitesimal, the following limits are calculated
(1) Limx squared cos1 / X and then x → 0
(2) Under Lim arctanx / X is x →∞

(1) X ^ 2 is infinitesimal, cos1 / X is bounded function, and the product of infinitesimal and bounded function is infinitesimal, so we directly get Lim x ^ 2cos1 / x = 0
(2) 1 / X is infinitesimal, arctan x is a bounded function, so the limit is 0
This way, there is no more detailed process, because you can get it directly