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[2014-11-19. : 11:55 am]

Moose -- MasterJohnny

MasterJohnny shouted: Mini Moose 2707 I don't think this is true if we are dealing with infinite sets

This is true, I stand corrected for infinite sets. card(R) = card(Rⁿ) for n < inf

[2014-11-19. : 6:25 am]

Fire_Kame -- demon's professor could probably lend a hand :awesome:

[2014-11-19. : 6:24 am]

MasterJohnny -- well technically we have made like no progress to Dem0n's problem...

[2014-11-19. : 6:17 am]

NudeRaider -- Stop having intelligent discussions in the shoutbox, I'm starting to feel dumb whenever I visit SEN.

[2014-11-19. : 4:59 am]

jjf28 -- Dem0n

Dem0n shouted: Does each element in set A have to map to the same positioned element in set B? Or can I cross-map stuff?

may as well, it would be very hard for you to show that you're covering all elements otherwise

[2014-11-19. : 4:59 am]

MasterJohnny -- what does cross map mean?

[2014-11-19. : 4:58 am]

Dem0n -- If I can cross-map it, I have no idea how to figure out which elements are mapped together

[2014-11-19. : 4:58 am]

jjf28 -- well, k^2 where k ∈ N ne ways

[2014-11-19. : 4:58 am]

Dem0n -- Does each element in set A have to map to the same positioned element in set B? Or can I cross-map stuff?

[2014-11-19. : 4:58 am]

MasterJohnny -- then A is just like a shift of natural numbers

[2014-11-19. : 4:58 am]

MasterJohnny -- I think B is the same thing as the natural numbers

[2014-11-19. : 4:57 am]

MasterJohnny -- i wonder if you're allowed to change B a little

[2014-11-19. : 4:55 am]

jjf28 -- write out some elements from each set, find a formula that relates them... will show that every a maps to a b

[2014-11-19. : 4:46 am]

Dem0n -- do algebra on wat

[2014-11-19. : 4:46 am]

MasterJohnny -- i have no idea how to create the bijective function lol

[2014-11-19. : 4:45 am]

jjf28 -- non infinite sets? do ur simple algebras demin

[2014-11-19. : 4:44 am]

Dem0n -- Form a bijection to prove that A = { 2k - 3 | k >= 0 ∈ Z } and B = { k² | k ∈ Z } are equal.

[2014-11-19. : 4:40 am]

MasterJohnny -- what was the problem?

[2014-11-19. : 4:39 am]

Dem0n -- well fuck lul

[2014-11-19. : 4:39 am]

MasterJohnny -- yeah so...

[2014-11-19. : 4:39 am]

jjf28 -- https://proofwiki.org/wiki/Integers_are_Countably_Infinite

[2014-11-19. : 4:38 am]

MasterJohnny -- unless the book tells you somewhere

[2014-11-19. : 4:38 am]

MasterJohnny -- you have to be creative and make your own bijective function

[2014-11-19. : 4:36 am]

jjf28 -- delete facebook, lawyer up, and hit the gym

[2014-11-19. : 4:34 am]

Dem0n -- How do I know which elements in sets A and B should be mapped together?

[2014-11-19. : 4:33 am]

MasterJohnny -- but if they are countable they have cardinaility less than or equal to the natural numbers...

[2014-11-19. : 4:33 am]

jjf28 -- http://en.wikipedia.org/wiki/Countable_set

[2014-11-19. : 4:32 am]

jjf28 -- so long as the sets are countable*

[2014-11-19. : 4:32 am]

MasterJohnny -- wut?

[2014-11-19. : 4:31 am]

jjf28 -- so long as the set is countable they can have different infinite cardinatilities IIRC

[2014-11-19. : 4:22 am]

jjf28 -- that R and RxR are unequal... assuming I remember a thing about set operations

[2014-11-19. : 4:20 am]

Fire_Kame -- Mini Moose 2707

Mini Moose 2707 shouted: Delete facebook, lawyer up, hit the gym

sound advice

[2014-11-19. : 4:20 am]

Fire_Kame -- mt

[2014-11-19. : 4:20 am]

Fire_Kame -- jjf28

jjf28 shouted: hey now, I wanted to use that when he asked a follow up

sound advice

[2014-11-19. : 4:20 am]

MasterJohnny -- jjf28

jjf28 shouted: {1, 2, 3} != {1, 2, 3, {1, 2}, {1, 3}, {2, 3}}

whats this suppose to teach me

[2014-11-19. : 4:19 am]

jjf28 -- {1, 2, 3} != {1, 2, 3, {1, 2}, {1, 3}, {2, 3}}

[2014-11-19. : 4:17 am]

MasterJohnny -- like R and RxR have the same cardinalities i think

[2014-11-19. : 4:17 am]

MasterJohnny -- Mini Moose 2707

Mini Moose 2707 shouted: Cartesian product multiplies the cardinalities

I don't think this is true if we are dealing with infinite sets

[2014-11-19. : 4:10 am]

Moose -- He does fear them. He's so scared he doesn't go. -_-

[2014-11-19. : 4:09 am]

jjf28 -- learn to phear your theory class dem0n, or it will kick ur ass

[2014-11-19. : 4:05 am]

Moose -- Dem0n wants to write a birektion

[2014-11-19. : 4:05 am]

Moose -- Also, you meant inrektion and surektion :moose:

[2014-11-19. : 4:03 am]

jjf28 -- hey now, I wanted to use that when he asked a follow up

[2014-11-19. : 4:03 am]

Moose -- Delete facebook, lawyer up, hit the gym

[2014-11-19. : 4:02 am]

jjf28 -- sure, show injection and surjection

[2014-11-19. : 4:01 am]

Dem0n -- Anyone know how to write a bijection between two sets to prove they're equal? D:

[2014-11-19. : 4:00 am]

Moose -- December 26th

[2014-11-19. : 3:59 am]

jjf28 -- May

[2014-11-19. : 3:58 am]

Fire_Kame -- when is it too early to start playing Christmas music

[2014-11-19. : 3:27 am]

Dem0n -- how the fuck yo

[2014-11-19. : 3:27 am]

Dem0n -- ∏i=1 -> ∞, 2(1/2ⁱ)

[2014-11-19. : 3:17 am]

Moose -- And you're done

[2014-11-19. : 3:17 am]

Moose -- Cartesian product multiplies the cardinalities

[2014-11-19. : 3:17 am]

Dem0n -- idk

[2014-11-19. : 3:17 am]

Moose -- So what's the problem?

[2014-11-19. : 3:16 am]

Dem0n -- I understand why R is larger than Z. It includes all the real numbers, whereas Z only includes integers.

[2014-11-19. : 3:15 am]

Moose -- Well, work on why R has a larger cardinality than Z, worry about the cartesian products later

[2014-11-19. : 3:13 am]

Dem0n -- no

[2014-11-19. : 3:13 am]

Moose -- Do you even aleph number?

[2014-11-19. : 3:11 am]

Dem0n -- How do you know? I don't know how to quantify that

[2014-11-19. : 3:10 am]

Moose -- Z x R

[2014-11-19. : 3:10 am]

Dem0n -- Which has a larger cardinality, Z² or (Z x R)? lel

[2014-11-19. : 3:08 am]

Moose -- The number of elements in a set, basically.

[2014-11-19. : 3:07 am]

Dem0n -- wtf is cardinality

[2014-11-19. : 2:30 am]

Roy -- http://i.imgur.com/FyNDOKT.png

[2014-11-19. : 2:27 am]

Roy -- The skinny of it is: with great power comes great responsibility.

[2014-11-19. : 2:25 am]

Dem0n -- I have no idea what that says

[2014-11-19. : 1:49 am]

Moose -- const int*const Method3(const int*const&)const; // const corREKTness

[2014-11-19. : 1:49 am]

Moose -- I just wanted to ask if you're ready for

[2014-11-19. : 1:48 am]

Dem0n -- Mini Moose 2707

Mini Moose 2707 shouted: Where is Dem0n, someone get me Dem0n

wut

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