4

6. Show that the set of all finite subsets of Q is countable....

Question

6. Show that the set of all finite subsets of Q is countable.

6. Show that the set of all finite subsets of Q is countable.



Answers

Show that the set of all finite bit strings is countable.

So we have a set that's called a just accountable I would take s which is a subset of a But that means that the car the night of s he's lower equal than they can. I d away because as he's a subset away and they can tell right away is just I live with zero because a is countable so that leaves two possibilities there Either s he is finite or as is countable

Let's follow these construction we put be zero to be the empty set. Now from a minus V zero, we take some element in some way. Let's say randomly on element X E X one course, be zeros empty. So when we remove nothing from A which left away in a is an infinite set. So while there are infinitely many elements, let's just take one. Let's call it X one. Then we put the one to be the said That only contains thes element X one. Now from a minus B one again, we take in some way on Element X two again, eh? As infinitely many numbers, I mean elements and we're not considering the elements of the one which is that just x one so well from infant. Infinitely many, we just remove one. So there are still in Fridley many, So we can take our next to say and then we put be, too to be said that contains X one and X two, and we keep repeating this process from a minus B n. We can still take some element because bien is going to be fine at, and so I am honest B and is going to be infinite. So there is something. This means that this process never stops because every bien again it's financially contents. Exactly. The elements x one x two all the way up to accent and so an A minus bien. He's still infinite. So there must. There must be something and in a month's bien, which means that we can take another element. Now we have the sequence off sets B one B two B C, which essentially means we have a sequence x one x two x three all the way up to Infinity because the process it never stops. So formally. Write this that Big B as the union off these sets bien But it's just means they were taking the said that contains x one x two, x three and so forth, which is an infinite set because the process never stopped. And he's countable because, well, we haven't admiration. We have x one x two x three Salt Well, there's objection with that, plus where X and goes to end and saw this set. Big B is a subset of a discounted Lee infinite as we wanted to see

So we're given comfortably. Many sets a n which accountable, and we want to show that their union is still countable, so the countable union of comfortable sets is still accountable. So to do that, let's fry the diagram where we have in the first column the elements off the set a one. So let's call them a one. A two, a three and so forth, then another column. You write the elements off the set a two. Let's call them B one B two B three and so forth. Then another call on the sets of a three. C wants to see three and we completely the ground. The diagram In this way. Now here, let's assume that all the sets a narrow, infinitely comfortable and all the elements are different because that's the hardest case. Because if some of the sets a we're fine, it, then that's not a big deal. The union off finance sets you still finance, so that doesn't change anything. And if there are some other lap ings between the sets, so if one element is both in some a one and a two, well, when we're uniting them, the union is Moeller, then it will be if all the sets were different. So the set where all the kids were all the sets are infinitely comfortable And all these joint is the hardest possible case. So let's assume that So all these a wanted to be three and all these numbers are all different. So the union of all the sets a wanted to a three and so forth We decide that contains all these numbers They wanted to be one and so forth. So now we want a way to enumerates these numbers. But again here the trick is going by diagonal enumeration. So this first element here we call it X one. Then we proceed diagonally So these x two and we go diagonally This is X three and then we proceed by the diagonals disease called x four We going diagonals disease x five Keep going Diagonals, thes xx and so forth. So, by drawing these diagonals, we're leasing all the elements off this union. Now the union ofall the end is going to be the set that contains x one x two x tree and so forth. And because a while we've laid out this diagram all these ex Sonics. Two extra A Are all the elements off these union when out is an enumeration off the elements of the union, and so it is comfortable.


Similar Solved Questions

5 answers
F 'S 4 Gronger GC'C Inan Fik 6 Which ofthe following is the stronger Bronsted- Lowry acid: HNOs or HNOz Give reasons.Which of the following is the stronger Bronsted- Lowry base: NH; or HzO. Give reasons.
F 'S 4 Gronger GC'C Inan Fik 6 Which ofthe following is the stronger Bronsted- Lowry acid: HNOs or HNOz Give reasons. Which of the following is the stronger Bronsted- Lowry base: NH; or HzO. Give reasons....
5 answers
Mume Valcnce ElectronFholecular plpola 0i HonpolatMolecul PolatomisThr Central Atomhas howMiny checahyeaMoltculzt GcomelreLetuli StructureOrbltl Geometrypalrirbondlngpulra7lona palatnbandlng palmtanmOnbrinbonding palrs?bondinpulr?Baln? bonding palra?Jona pauratbonding pairs?ch;ciPaln? bonding pairs?Ypela?
Mume Valcnce Electron Fholecular plpola 0i Honpolat Molecul Polatomis Thr Central Atomhas howMiny checahyea Moltculzt Gcomelre Letuli Structure Orbltl Geometry palrir bondlngpulra7 lona palatn bandlng palmt anmOnbrin bonding palrs? bondinpulr? Baln? bonding palra? Jona paurat bonding pairs? ch;ci Pa...
5 answers
Problem l: Find the Laurent series expansions of the following analytic func- tions in the indicated regions:f(z) = 22 when 0 < |z| < 1 z _ (b) f(2) = (22 _ 2) cos (4) when 0 < |z| < 0;(c) f(z) = when 0 < Iz _ 1/ < &; (2 = 1)2(d) f(2) = when 0 < |z/ < 1; 24(1 + 2)
Problem l: Find the Laurent series expansions of the following analytic func- tions in the indicated regions: f(z) = 22 when 0 < |z| < 1 z _ (b) f(2) = (22 _ 2) cos (4) when 0 < |z| < 0; (c) f(z) = when 0 < Iz _ 1/ < &; (2 = 1)2 (d) f(2) = when 0 < |z/ < 1; 24(1 + 2)...
5 answers
Foui)343An ckectron is moving ang the s-axis in the pwsitive X dircction. An electric field is directed in the +y direction. Which direction MSI the minimum strengrh magnetic field be pointed t0 Jllow thc elcctton t0 move undellected:(A) +>(Bi ~y(( +<(I) 52(F' X* X
foui) 343 An ckectron is moving ang the s-axis in the pwsitive X dircction. An electric field is directed in the +y direction. Which direction MSI the minimum strengrh magnetic field be pointed t0 Jllow thc elcctton t0 move undellected: (A) +> (Bi ~y (( +< (I) 52 (F ' X * X...
5 answers
QUESTION 5Whicn of the following is true given Ac % -2.71 kcal fortne reaction: Caco 3 (s) + H Tne cissclution of CaCO3 is spontaneous under che stanoard condition Tne Ksp ` value can be estimazed %y ex? (-AGORT} LG 0 wnen tne acove reac-ion in equilibrium All of aboveCa 2 - HCO 3
QUESTION 5 Whicn of the following is true given Ac % -2.71 kcal fortne reaction: Caco 3 (s) + H Tne cissclution of CaCO3 is spontaneous under che stanoard condition Tne Ksp ` value can be estimazed %y ex? (-AGORT} LG 0 wnen tne acove reac-ion in equilibrium All of above Ca 2 - HCO 3...
5 answers
8 3 1 dimensions alejedas teranseters neededcomer H piece sides ~of cardboard, Ir 1heose box area Eaesi sqoauerne of 306 centnetors cubic contimeters, made Into V cardboar should 2 2-cenuimeter stant square from each
8 3 1 dimensions alejedas teranseters needed comer H piece sides ~of cardboard, Ir 1heose box area Eaesi sqoauerne of 306 centnetors cubic contimeters, made Into V cardboar should 2 2-cenuimeter stant square from each...
5 answers
Consider the surface f(z,y) = I 31 12y. points) Find the first partial derivatives Find the gradient vector Vf(z,y).points) Find the second partial derivatives_
Consider the surface f(z,y) = I 31 12y. points) Find the first partial derivatives Find the gradient vector Vf(z,y). points) Find the second partial derivatives_...
4 answers
[Rovlot Tonics][Rafatoncos]Use the Relerenccs to #ccers Important values H necded for thbs quectlonWhich of the properties bclow apply to the following polymer?Choose all that apply:Oasubstituted polyethylene Oan addition polymer Oapolymer formed by splitting out water polyester polyamideSubmll AnswerRetry Emlro Oiouamora group attempta romaining
[Rovlot Tonics] [Rafatoncos] Use the Relerenccs to #ccers Important values H necded for thbs quectlon Which of the properties bclow apply to the following polymer? Choose all that apply: Oasubstituted polyethylene Oan addition polymer Oapolymer formed by splitting out water polyester polyamide Subml...
5 answers
@robbleen 2 (30 Vtl1e6Ablock supponted by Inic tionles: tollcz1033805.5' Kune a5 shown on Ihc figute , Dctcrthinc thc #txjic coellicient of hticton V #tthc coniact B if the Blocck 6 on the verpe ol sliding down thc incline,Ja25
@robbleen 2 (30 Vtl 1e6 Ablock supponted by Inic tionles: tollcz1033805.5' Kune a5 shown on Ihc figute , Dctcrthinc thc #txjic coellicient of hticton V #tthc coniact B if the Blocck 6 on the verpe ol sliding down thc incline, Ja 25...
4 answers
If f(z) = 4x + 3 then f-'(z)Use these two functions to find:f(1) =b. f-1(1) =Previewc. f[f-1(1)]d. f-1[f(1)]
If f(z) = 4x + 3 then f-'(z) Use these two functions to find: f(1) = b. f-1(1) = Preview c. f[f-1(1)] d. f-1[f(1)]...
5 answers
Particle of weight 7 N is held stationary with a force P newton at an angle b=28 degrees on a frictionless inclined plane with a = 33 degrees. Find the magnitude (in newton) of the normal reaction force of plane on the particleAnswers must be rounded off to two decimal places.
particle of weight 7 N is held stationary with a force P newton at an angle b=28 degrees on a frictionless inclined plane with a = 33 degrees. Find the magnitude (in newton) of the normal reaction force of plane on the particle Answers must be rounded off to two decimal places....
5 answers
Q 5 PoiNTSPreMDusANsVarHr10 [email protected] Cncinsoyeme] Vicuhoreonin lorces acunocjng? crnistcr thjtinitally Gatnanbuithai Dor Mocnr aeroneTriconiasdcorMjonitudesF =4-10and tneundiatcd JnalesADaeo"Kori DJnscanistecEherthee rcecduntnoFny 4Gdicnicement'67.,031Mcnz I6cnrIhe indniduz Aone Une RontcnedurinearcolacemencEnnoenecem E-dinn 7 2
Q 5 PoiNTS PreMDusANsVar Hr10 7.P.014. Liencs [email protected] oeloy Cncins oyeme] Vicu horeonin lorces acuno cjng? crnistcr thjt initally Gatnanbuithai Dor Mocnr aerone Triconiasdcor Mjonitudes F =4-10 and tneundiatcd Jnales AD aeo" Kori DJns canistec Eherthee rcecduntno Fny 4G dicnicement...
5 answers
Winat series of reections would provide 1-bromo-3-propyl benzene as the major product; starting with benzene?Select onezAICI]Brz. FeBra Zn(Hg) , HCIBrz. FeBraAICI Zn(Hg) . HCIAICIazn(Hg). HCI Brz, Fe8raa NICl B7z FsBraEiz Esexs'NCL
Winat series of reections would provide 1-bromo-3-propyl benzene as the major product; starting with benzene? Select onez AICI] Brz. FeBra Zn(Hg) , HCI Brz. FeBra AICI Zn(Hg) . HCI AICIa zn(Hg). HCI Brz, Fe8ra a NICl B7z FsBra Eiz Esexs 'NCL...
5 answers
Give the answer to six decimal placer26. Solve the right triangle]1s30 304 #l7 48
Give the answer to six decimal placer 26. Solve the right triangle] 1s30 30 4 #l7 48...
5 answers
The grach d the boundary equatons fr te System Inequahes shainLocaia Ihe Idemty i by inding the corners solulon Igan,6x + 79> 12 5k*Y28 40,Y20Wnal a12 Ine comar points ol the dulon tegon?
The grach d the boundary equatons fr te System Inequahes shainLocaia Ihe Idemty i by inding the corners solulon Igan, 6x + 79> 12 5k*Y28 40,Y20 Wnal a12 Ine comar points ol the dulon tegon?...
3 answers
E 19 in section 8.3 of your textbook, about the nervous basketball player; using the following data: throw; then her probability of making the next one is 0.6. On the other hand, If she missed the last free is 0.5_ throw; then her probabilityMakes the Free Throw and that state 2 is Misses the Free Thrownatrix for this Markov processe-throw shooting probabilities for this player: W =
e 19 in section 8.3 of your textbook, about the nervous basketball player; using the following data: throw; then her probability of making the next one is 0.6. On the other hand, If she missed the last free is 0.5_ throw; then her probability Makes the Free Throw and that state 2 is Misses the Free...

-- 0.020938--