Is it true that the six equivalent presumptions of the completeness of real numbers extend to plural numbers? How to prove them

Is it true that the six equivalent presumptions of the completeness of real numbers extend to plural numbers? How to prove them

Since complex numbers have no size, the principle of supremum and monotone boundedness do not hold in complex fields
The others are true, because the complex field can be regarded as equivalent to R ^ 2, and the remaining properties in R ^ 2 are true

The two trains, a and B, set out from two places 500 kilometers apart at the same time and run in opposite directions. They meet each other in 2.5 hours. How many kilometers does car a travel per hour and car B travel per hour

If the average of six numbers is 90, if one of them is changed to 10, the average will be 80. What is the number?

This number
=（6×90-6×80）+10
=60+10
=70

If the natural numbers are arranged according to the following rules, the position of 2008 is the third______ Line number______ First column second column third column fourth column First line 1 2 9 10 The second line 4 3 8 11 The third line 5 6 7 12 The fourth line 16 15 14 13 Line five 17     … …          

2008 = 442 + 72, 442 = 1936, then the number starts from the 45th row in 1937, turns from the 45th column in 1981, and the position of 2008 is the 18th row and the 45th column in the 18th row

The number of 7 0.01, 3 0.1 and 5 0.001 is ()

0.375

On a map with a scale of 15000000, the distance between a and B is 8 cm. On another map with a scale of 1:4000000, how many cm is the distance between a and B?

8 △ 15000000 = 40000000 (CM); 40000000 × 14000000 = 10 (CM); answer: the distance between a and B is 10 cm

The gate of a factory is shown in the picture, in which the quadrilateral ABCD is a rectangle, and the upper part is a semicircle with ab as the radius, where ad = 2.3, ab = 2.3
We need mathematical language

No picture!

There are 4500 tons of coal in pile a, pile B and pile C. when 20 tons are taken out of pile a and put into pile B, 30 tons are taken out of pile C and put into pile B
The weight of coal in pile a is 1 / 8 less than that in pile B, and pile C is 2 / 7 more than that in pile a
Is it OK to count

The solution of the equation assumes that there are x tons of coal in coal pile B, then the coal pile a is 8 / 7 * x tons. According to the title meaning, the solution is: 8 / 7 * x + 8 / 9 * x + x = 4500, and the solution is: x = 1500, then: 1500 * 7 / 8 + 1312.5 〈 the coal pile a has: 1312.5 + 20 = 1332.5 〉 the coal pile B has: 1500-20-30 = 1450 〉 the coal pile C has: 4500-1332.5-1450 = 1717

No matter how many positive numbers there are, their arithmetic mean must not be less than the geometric mean. This is the definition of mean inequality. How can we deduce it?

Geometric mean: GN = (A1A2... An) ^ (1 / N)
Arithmetic mean: an = (a1 + A2 +... + an) / n
Specific proof process, more than the number of words, see resources

The speed ratio of a and B is 7:9. When a runs 72km less than B, how many km per hour does a and B run?
No equations!

The distance between the two places: 72 ÷ (9 / 16-7 / 16) = 576km
Speed and speed: 576 △ 6 = 96 km / h
7+9=16
A speed: 96 × 7 / 16 = 42 km / h
B speed: 96 × 9 / 16 = 54 km / h