The completeness of real number set can be changed into continuity, which can be simply understood as a smooth curve on the number axis, and the curve is composed of rational numbers and irrational numbers, so it is not continuous to take out a rational number set or an irrational number set alone.

ε is generally pronounced Epsilon, which generally means the minimum value.

Is it really in the middle? ε& gt； 0,? Xo∈A, making XO >；; S-ε。 Then S is the supremum of A: it can be understood that there is a very small number, even about 0, which makes S minus this number still greater than xo, that is to say, xo will be less than S no matter what value it takes, and this S will be infinitely close to xo when it takes the maximum value.

Any group of non-empty real numbers A with an upper bound must have an upper bound: I don't know how to explain this for too long.

Regarding the law of function association, idempotent law and duality principle, if you are majoring in mathematics or plan to engage in related industries in the future, you'd better master it. If you are preparing for the exam, just find out or ask the teacher if there are any test sites.

D(f) refers to the set of domain, that is, the set of all numbers that can be obtained by independent variables, and R(f) is the set of range, that is, the set of function results.

Shu Gao is a sinkhole. I don't know until I spend some time. It's normal to ask the teacher. The teacher has passed. He naturally knows how powerful you are and won't think of you. If you really don't want to ask, it is also a good choice to go to the library to find reference books or ask seniors and sisters.