What is the relationship between approximation and accuracy

The more bits of approximation, the higher the accuracy

Solution: let a and B be sets of natural numbers Mapping f: a → B
1. Let both sets a and B be sets of natural numbers, mapping f: a → B maps the element n in a to the element 2 ^ n + N in B, then under the mapping, the elements in a are______ Corresponding to the element in B
2. Given the set a = {1,2,3, K} B = {4,7, a ^ 4, a ^ 2 + 3A} and a ∈ n, K ∈ n, X ≤ a, y ∈ B, map f: a → B such that the element Y in B = 3x + 1 corresponds to the element X in a, and find the value of a and K
3. If the mapping f: a → B, where a = {- 3, - 2, - 1,1,2,3,4} corresponds to any a ∈ a, there is a unique | a | in B and it corresponds to it, the range of the mapping is obtained

1) Fill in "n unique" corresponding to element 2 ^ n + N in B, that is, n → 2 ^ n + n
2) 1 → 4,2 → 7,3 → 10, K → 3K + 1, so, or a ^ 4 = 10, or a & # 178; + 3A = 10, the former a is an irrational number, which is not consistent with the image of K, so only a & # 178; + 3A = 10, that is, a = 2, (a = - 5 is not a natural number), the fourth power of 2 = 16,3k + 1 = 16, k = 5,
A: a = 10, k = 5,
3) | - 3 | = 3, | - 2 | = 2, | - 1 | = 1, so B = {1,2,3,4}

Multiplication of two numbers, the base is the same, the index is not added

In the multiplication of integers, what should we do if the exponents are different? Will the base be added and the exponents added, or the base exponents remain unchanged
For example: 3 (quadratic power of 4x + quartic power of 3x)

I don't know if you're talking about this formula. If it is, then this formula is the multiplication of a monomial and a polynomial, the second power of X multiplied by the fourth power of X. we can get the sixth power of X by multiplying the power of the same base, keeping the base unchanged and adding exponentially. If it is the second power of x plus the fourth power of X, they are not the same kind, Can't merge, then this formula is the simplest

Find the n-th power of the absolute value of the product of the reciprocal of 3 and 1 / 3 opposite numbers (n is a positive integer)

The inverse of 3 and 1 / 3 = 10 / 3 is - 10 / 3, the reciprocal of 10 / 3 is 3 / 10, and the product of them is (- 10 / 3) (3 / 10) = - 1
|-1 | = 1 ^ n (n is a positive integer) = 1
The final result is 1

How to prove that a rational number set is countable?

Let an = {1 / N, 2 / N, 3 / N,... M / N...}, q + = any union of an, be a countable set
Let the mapping from $: Q + to Q -, $(x) = - x, X belong to Q +,
Obviously $is a one-to-one mapping from Q + to Q -, so Q + and Q - are equivalent
And q = q + and q-union {0}

It is proved that the rational solution of the polynomial equation with integral coefficients whose coefficient of the highest degree is 1 must be an integer
It's a problem of elementary number theory. The coefficient of the highest degree term of the equation with one variable is 1. How to prove that the rational root of this equation must be an integer?

Let x = A / B, a and B be integers, and (a, b) = 1
I'll put X in the equation and multiply B ^ n on both sides
a^n +k1a^(n-1)b+.+k0a0b^n=0
On the left, only a ^ n does not contain B
So b|a ^ n
b=(b,a^n)=1
X = a is an integer

Polynomials with rational coefficients are countable
Just started to learn real variable function, do not appear after the content

This seems to be an example in my book Let me give you a simple idea. Instead of writing the strict proof process, let's see if it's right. In fact, rational coefficient polynomials can be divided into order 0, order 1, order 2 Order 0 is the set of rational numbers Q. The combination of order 1 and order 0 requires two rational numbers to determine, which is actually Q

F (x), G (x) are polynomials over the rational field, and f (x) is irreducible over the rational field,
If there is a complex number a such that f (a) = g (a) = 0
Proof: F (x) | g (x)

If f cannot divide g, then let H (x) be the nonzero remainder polynomial after g (x) is divided by F (x), that is, G (x) = f (x) F1 (x) + H (x), then DEG H

In this paper, Eisenstein discriminant method is used to judge the integer coefficient polynomials
For example, when judging f (x) = x ^ 6 + x ^ 3 + 1, why use f (x) = f (y + 1) to minimize the number of items with zero coefficient? Is this more accurate?

Eisenstein's criterion seems to say that (for Z [x]), we have to find a prime P, P does not divide the coefficients of the polynomial of the highest degree, P divides the other coefficients, and P ^ 2 does not divide the constant. You can't find a prime P so that P divides the constant (the constant is 1). Let x = y + 1 and write it as a polynomial of Y, then you can take P = 2

What is the relationship between approximation and accuracy