Question

@satellite73 need help with something link in comments

Answer 1

http://math.stackexchange.com/questions/751410/prove-f-infty-a-infty-rightarrow-b-infty-is-a-bijection

Answer 2

can you please take a look at this... I'm kind of overwhelmed for Aoo -> boo bijection using a theorem

Answer 3

like the sequence won't terminate for infinity... that could go on forever and ever

Answer 4

i can look, but frankly i have no idea what \(f_{\infty}\) is
neither do i know what \(B_{\infty}\) is etc

Answer 5

that's the function infinity going from a -> b ... because that theorem suggests that there is an injection

Answer 6

i did however find this, which might be of some use

Answer 7

so it's a one to one pmap

Answer 8

O_O that's the same document I am viewing

Answer 9

all I could point out of this mess is that the sequence goes on forever and since it's a bijection... there is a surjection map and an injection map. but how would I fit those pieces?!!?!!?!?

Answer 10

the sequence doesn't stop at a point.

Answer 11

this seems slightly more readable and i think addresses your point above
http://www.whitman.edu/mathematics/higher_math_online/section04.09.html

Answer 12

so the sequence for the infinity goes on forever... so how do I draw an injection surjection on this bad boy?

Answer 13

reading the second one, my head is spinning a little

Answer 14

my entire mind is spinning over this... what the heck do I do?! O_O the A+ and the A- were given... OH wait I know.. what if we can't prove A oo and B oo because it breaks the theorem. That might work ? right? we can always prove or disprove a statement.

Answer 15

if i read this five or six more times i might understand it
i am sort of getting the gist of it (sort of)

Answer 16

are you trying to prove something else? or are you trying to comprehend this theorem?

Answer 17

it looks like you are supposed to use the theorem, not prove it, right?

Answer 18

I am trying to prove that there is a bijection for foo :A_oo -> B_oo

Answer 19

yes I am trying to use the theorem, but based on those hints... those sequences for A and B are going to continue like crazy... so there is an injective map and a surjective map, but I don't know how to draw it out or make it pop appear

Answer 20

i am stuck sorry

Answer 21

same here D: and I know my peers aren't going to score. you know something isn't right when everyone failed themidterm.. 25 out of 80 is the average and on the last 2 assignments 3 out of 10 w th

Answer 22

@Callisto @ganeshie8

Answer 23

o_________O I sort of have it but I can't piece it together somehow

Answer 24

somehow I have to apply the definitions of surjection and injection on that massive sequence and since it doesn't terminate at all.. it can go on forever and ever... until the earth and the whole universe comes again and again.

Answer 25

like (a,b,a_1,b_1,a_2,b_2,a_3,b_3................... on and on

Answer 26

@zzr0ck3r help me D:

Answer 27

I'm about to eat and that looks like Chinese to me at the moment, ill come back after dinner:)

Answer 28

what is \(A_\infty,f_\infty\)?

Answer 29

the A_oo is supposed to be the set A infinity

so we had A+ and A- already proven with the theorem

Answer 30

so there's a function infinity : A infinity -> B infinity and I have to prove that it's a bijection. I sort of see where this is going....it's just that writing the sequence that is going to go on forever is making me scratch my head. and this fjdsajsdlfj is due on Monday and I'm throwing every attempt at this

Answer 31

my prof claimed that this is a 2 line proof and use the previous example as a guideline which is the f_ : A_ -> B_

Answer 32

Don't you get it? We need to know what these sets are to actually do this proof!

If A is natural numbers and B is real numbers, it can't be done!

Answer 33

so we have an impossible proof in our hands. :O

Answer 34

got it ! A and B are disjoint sets. @wio

Answer 35

The set of all irrational numbers and the set natural numbers are also two disjoint sets, and there is no bijection between them.

Answer 36

so in the end it's impossible to do this proof.. because A and B are totally different sets.. so there isn't a bijection being produced.. no bijection --> no surjection... no injection either

Answer 37

Well, can you tell us anything else about A and B other than they are disjoint?

Answer 38

I'm reading the theorem.. it assumes that A and B are disjoint...then there is a sequence...

Answer 39

The problem isn't the theorem, the problem is the question isn't very clear

Answer 40

oh...

Answer 41

I've talked to someone on stackexchange chat they say that there is a \[f_n : A_n \rightarrow B_n\] but there isn't any infinity at all.

Answer 42

strange why was I given the oo question... all I have out of it is that the sequence doesn't terminate and goes on forever.

Answer 43

perhaps we could subsitute the infinity for the n and then show that it's a bijection !?!

Answer 44

all the stuff I wrote are the notes and my attempt for that infinity bug thing

Answer 45

!!!! I am lost. period. Maybe I should wing, turn it in on Monday and do corrections when I get it back.. T___T