Question

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

Answer 1

@experimentX

Answer 2

lol ... still not answered?

Answer 3

I have heard this theorem before in Stefan Abott's Analysis book

Answer 4

but I still have no clue what the fsdklfjlsdk;fj is going on... it's not like the Cauchy theorem proof.

Answer 5

*bangs head* 2 line proof on each case.. HOW?!

Answer 6

and that's the three hints from the question... 2 line proofs 0)0x-0sf

Answer 7

http://en.wikipedia.org/wiki/Cantor%E2%80%93Bernstein%E2%80%93Schroeder_theorem

Answer 8

I even tried that on my previous attempt... x.x

Answer 9

nugh... I need my misery to end -_- on this -_-!

Answer 10

your handwriting is terrible ...

Answer 11

don't have mathblog or something??

Answer 12

I was writing and sleeping at the same time... that's how boring my prof was

Answer 13

hahaha ... lol

Answer 14

so how the heck can this problem be approached

Answer 15

hmm ... this cantor-berstein-sch ... thing?

Answer 16

eeyup

Answer 17

hold on a sec ... a guy on M.SE is buggin me. let me handle him first.

Answer 18

k

Answer 19

link?

Answer 20

lol ... where did i click. here
http://math.stackexchange.com/questions/780600/double-integral-intervals/780606?noredirect=1#comment1618997_780606

Answer 21

there seems to be couple of proofs on wikipedia article ... but not understood myself. :S

Answer 22

wahhhh!!!!!!!!! x.x

Answer 23

it's witchcraft lol

Answer 24

i read this thing on Abott's understanding analysis ... along with this Baire Category theorem or somthing like that.

Answer 25

@ganeshie8 any ideas?!

Answer 26

@zzr0ck3r ?? @miracrown??

Answer 27

i need to study this myself ... let's see if I can get something understandable out of it.

Answer 28

ins't King George around??

Answer 29

The clue lies in the definition of f∞, where f∞ has been defined to be a restriction of the function f.

Answer 30

that' slike the restriction of the domain and codomain ... narhgdisafiojweioureiw

Answer 31

@KingGeorge I FOUND MY NOTES!!!!!!!!!!!!!!!!!!!!!!!! :O

Answer 32

@Kainui

Answer 33

@UsukiDoll is proof on your note is same as the one on wikipedia?

Answer 34

yeah but that still doesn't answer the bijection thing... all I know is that a bijection occurs when it's one to one (injection) and onto (surjection )

Answer 35

this isn't algebra lol ... where you could argue if Ker(T) = 0, then bijective

Answer 36

what the ._.

Answer 37

this proof sucks -_-

Answer 38

do you understand the proof of this Cantor–Bernstein–Schroeder theorem?

Answer 39

no ._. all I know is that there's cardinality x.x

Answer 40

@satellite73 maybe these scanned notes would help?!

Answer 41

@zzr0ck3r

Answer 42

non of the scans are loading for me....

Answer 43

what the!

Answer 44

the scans load fine... what the what the ...... ._________.!

Answer 45

it happens on my tablet. ill switch it up. if this is analysis stuff I would ask eliassaab hes a god at that stuff....

Answer 46

ugh this is only coo coo proof problem that is driving me buggy :(

Answer 47

@UnkleRhaukus would the scan notes help in some way?