1, in fact, basically just prove that F is bounded in [a, +∞] and there must be a maximum and a minimum.

At least one of them will appear in (a, +∞), otherwise it is a constant, which can be proved as follows:

3. First, understand the mathematical concept of "continuity". According to the mathematical definition, the function of point A must meet the following conditions:

( 1)? F(x) is defined in a neighborhood of point A, which can be infinitely small, but not zero.

(2)? lim(x->； a)？ f(x) =f(a)

As long as it meets the above item, it is defined as continuous.

Therefore, continuity is the concept of a single point. A function can only have one continuous point, and any other point is discontinuous (a little opposite).

Intuitive feeling), but according to the mathematical definition.

For example: f(x) = x 2 (x is a rational number), =-x 2 (x is an irrational number), and f (x) is continuous only at x=0.

Limit is the same, you just need to master its mathematical definition, and don't understand it as a philosophical concept.

4. Look at the definition

I don't agree with this statement. The concepts of "adjacency" and "continuity" here are vague and changeable.

Mathematical "adjacency" is generally aimed at countable sets, but for real numbers, there is no "adjacency" point.