We extend from ℚ≥0 to ℚ by another application of the method of ordered pairs, exactly as we did to extend from ℕ to ℤ. Thus, elements of ℚ can be written as ordered pairs of ordered pairs - we might for example write 1/2 as ((1,2),(0,1)). Explain how to construct the standard ordering < on the rational numbers in terms of the coordinates in these ordered pairs.

Q: Derive one-one correspondence between the real numbers in (0,1) and the set of irrational numbers in…

A: Both the sets that is real number in 0,1 and the set of irrational numbers in 0,1 are uncountable as…

Q: (a) How many nonnegative integer solutions are there to the equation ₁ + x₂ + x3 + x₁ = a? (b) How…

A:

Q: se a dire tional.

A: Introduction: A direct proof is a logical series of statements that demonstrate the truth or falsity…

Q: Which x satisfies both Ix - 31 &lt; 2 and Ix - 51 &lt; 1?

A:

Q: IfX~N(7,4), the P(15.364 ≤ (X-7)² ≤ 20.095) is

A: Given problem is :

Q: . The relation ⋆ means “this number written out in English has this many letters”. For example, 6 ⋆…

A: A relation R  on a set A is said to (1) Reflexive : forall x in A implies (x,x) in R . (2)…

Q: Sometimes it is necessary to find the coordinate of a point on a number line that is located…

A: Hey, Thanks for the question." Since you have posted multiple subparts, as per our guidelines we…

Q: a polygon with n sides has D diagfonals, where D is given by the function D(n)=n(n-3)divided by 2.…

A:

Q: Show that there are an infinite number of rational numbers between any two real numbers x and y with…

A: using Archimedean property to prove above therom...

Q: Tom wants to invest $500. He invests in a company that predicts his investment will double in value…

A: Initial investment is $500 and the money gets doubled in 3 years.

Q: 3. In the domain of real numbers, explain what the following statement says in English. A rational…

A: Given: The given statement ∀x∀yy&gt;x→∃zz is a rational number∧x&lt;z&lt;y To find: we need to…

Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

Q: Divide x-5²–7by x+2. Remember to state restrictions and a division statement at the end. [4 marks]

A: The problem is about simple polynomial division, so I used polynomial long division method to solve…

Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: The set of rational numbers is closed under division. True or False?

A:

Q: Find the equatians of the haranntal and vertical Reymptotes for the functien 2x -7x- 30 (x) - 20-

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: what is the maximum number of functions one can make from a set of n elements to a set of m elements

A: If |A|=n  And  |B|=m  Then the number of possible function from A to B is m^n.