Is limit equal to 0 equal to infinitesimal

Is limit equal to 0 equal to infinitesimal

Infinitesimal is X - > 0
If the limit is equal to 0, then a = 0
Don't confuse them

Is infinity the nonexistence of limit? What's the relationship between them?

Infinity means that any subsequence of the sequence or function tends to infinity and the limit does not exist. For example, y = x tends to infinity in R, while y = x * x does not exist in r but does not tend to infinity, because y tends to 0 in the interval from negative infinity to 0 instead of infinity

1. If the limit is infinite, does it mean that the limit does not exist?

Limit is defined as that when the independent variable tends to a certain point along a fixed direction, the function value is infinitely close to a certain value. So, is infinity a certain value? Obviously not. The reason why limit is infinity is that it usually corresponds to infinitesimal and is the reciprocal of infinitesimal. Limit either exists, is a certain fixed value, or is infinitesimal, that is, 0