There is a definition in a neighborhood (that is, a subset of the domain, which can be a certain length or infinite).
If a positive number m is given arbitrarily (no matter how big it is), there is always a positive number A, as long as x is suitable for the inequality 0 < │ x-x.
│ < a (or x > a), and the corresponding function value always satisfies │ F(X) │ > m, then the function F(X) approaches x at x.
Yes, it is infinite.
Simply put, the infinity of a function means that no matter how big a positive number you give, the function can always get a larger number than you give.
As for the problem mentioned by the landlord, zero multiplied by any number equals O, which is beyond doubt, including the special case of multiplying by infinity.
The problem of the landlord is that you regard O as infinitesimal, which will be mentioned when you seek the limit in higher mathematics learning. O can be regarded as infinitesimal.
Then the landlord should want to ask the question of multiplying infinity by infinitesimal.
Infinity and infinitesimal are hierarchical, including first-order infinity (infinitesimal) and second-order infinity (infinitesimal) ... so the limit of their products cannot be determined.
For example, X and X2 (square), when X approaches ∞ in the defined domain, the values of X and X2 are infinite, but obviously X2 grows faster than X, so X2 is infinite with higher order than X. As for infinitesimal, one tenth of X and one half of X2 approaching ∞ in X means infinitesimal of different orders, and obviously one half of X2 will decrease faster.
For example, for 1/X multiplied by X2, the limit of x approaching infinity is obviously x (infinity); If 1/X2 is multiplied by x at the limit where x approaches∞, it is obviously 1/X (infinitesimal).
Don't worry, let's pass the college entrance examination, which is the foundation of the university. ......