it up the intelligence quotient that make a math problem in english and solve it. why? it is different that solve a japanese math problem from make a math problem.
Let S be a set of rational numbers with the following properties:1) 1/2 is an element of S2) If x is an element of S, then both 1/(x+1) is an element of S and x/(x+1) is an element of SProve that S contains all rational numbers in the interval 0<x<1.
>>14 If x=m/n then 1/(x+1)=n/(m+n) and x/(x+1)=m/(m+n).
So, let q=m/n be an arbitrary rational number from the interval (0,1). Obviously we may assume that GCD(m,n)=1. Therefore by Euclidean Algorithm there is a finite sequence of rational numbers {q_i=m_i/n_i}_{i=1}^{n} such that q_1=1/2, q_n=q and for every i=1,...,n-1 one of the following holds:
m_{i+1}=m_i and n_{i+1}=m_i+n_i,
or
m_{i+1}=n_i and n_{i+1}=m_i+n_i.
It means that q_{i+1}=q_i/(q_i+1) or q_{i+1}=1/(q_i+1). And hence q_i \in S for all i. In particular, q=q_n \in S. The problem is solved.
Suppose we have such an equivalence relation is S. Given an element x of S, let C_x consist of all elements of S which are equivalent to x. Then all elements C_x are equivalent to one another , as follows from our three properties. Furthermore, you will also verify that if x,y are alements of S, then either C_x=C_y , or C_x,C_y have no elements in common. Each C_x is called an equivalence class. We see that our equivalence relation determines a decomposition of S into disjoint equivalence classes. Our first example of the notion of equivalence relation will be the notion of congruence. Let n be a positive integer. Let x,y be integers. We shall say that x is congruent to y modulo n if there exists an integer m such that x-y=mn. This also means that x-y is divisible by n. We write the relation of congruence in the form: xßy mod n. It is then immediately verified that this is an equivalence relation , namely that the following properties are satisfied:
1.For any positive integer k , give a proof of 7^kß1 mod 6
Monday, July 14, 2008 President Bush delivered a statement on the 10th anniversary of the International Religious Freedom Act at the White House. He expressed his continued support for the IRFA, discussed how bipartisan efforts in implementing the IRFA have elevated and institutionalized the promotion of religious freedom and the progress made to date, and called for renewed efforts to implement the IRFA.
The International Religious Freedom Act represented a bipartisan effort by Members of Congress, human rights groups, and religious leaders and communities to end religious persecution and intolerance. The main goals of the legislation were to provide the mandate, resources and tools to raise public awareness of religious persecution; generate consistent, effective United States Government action to end persecution and promote religious freedom; ensure that promotion of religious freedom was an integral component of our foreign policy; and create strong incentives for change by governments violating religious freedom.
President Bush also made a statement discussing the need for Outer Continental Shelf exploration to ease our dependance on foreign oil.
There is a finite number of towns in a country. They are connected by one direction roads. It is known that for any two towns, one of them can be reached from the other one. Prove that there is a town such that all the remaining towns can be reached from it.
u‚A‚‘A‚’@are@natural@numbers@‚‚Ž‚„@satisfing@‚…‚‘…‚’D ‚‚Ž‚„A‚A‚‘ are even@numbers and ‚’ is odd number. find the most small positive integral number satisfing ã‚~ã‚‘~ã‚’v
the intelligence quotient@of the white is 115 the intelligence quotient@of the yellow is 110(japanese is 118) the intelligence quotient@of the black is 90
Let m and n be integers greater than 1. Consider an m*n rectangular grid of points in the plane. Some k of these points are colored red in such a way that no three red points are the vertices of a right-angled triangle, two of whose sides are parallel to the sides of the grid. Determine the greatest possible value of k for any given values of m,n > 1.
Let m and n be integers greater than 1. Consider an m*n rectangular grid of points in the plane. Some k of these points are colored red in such a way that no three red points are the vertices of a right-angled triangle, two of whose sides are parallel to the sides of the grid. Determine the greatest possible value of k for any given values of m,n > 1.
Nobodody bothers to come here and answer your questions in English. People increase the chances to see and answer your questions in chat in English thread.