CrossClown

Suppose that f is a function and that f: [0,1] -> [0,1] defined by the piecewise function:

f(x) = x if x is rational

f(x) = 1 - x if x is irrational

Prove that f is continuous only at the point x = 1/2.

If f is a continuous function on a bounded set S then the function f is uniformly continuously on S if and only if it is possible to extend f to a continuous function on the cl(S).

I'm going to be flying Asiana Airlines for the first time and I just needed someone to clarify as to what they consider as a carry-on. I've checked their website and read through the description but I have a friend that told me they'll make you pay extra for a backpack. This confused me a little because I use a laptop backpack to bring my laptop everywhere and normally, other airlines wouldn't just ask for extra for things like that. I've flown Cathay and Korean Air, and they haven't given me problems about it. Can anyone clarify if Asiana will charge extra for my laptop backpack...?

I was in a hurry yesterday and I ended up buying soccer socks instead of regular tube socks, and I don't have time to go back and return them so I figured eh let's make it work somehow. I'm one of those people that like to wear black tube socks with shorts and I have socks of varying heights, ones half way between my knee and ankle, and I have ones that go all the way up to my knees (for those "who gives a f***" kind of days). So do you think I could make soccer socks work in the same fashion? They are black socks and they end up going above my knees but I figure I could just roll them down to below my knees.

I'm trying to figure the following question and I cannot, for the life of me, figure out where to even begin:

Given: Ik1={1,2,...,k1} and Ik2={1,2,...,k2}

Suppose that f:Ik1 -> Ik2 is a bijection. Show that k1=k2.

Cardinality is something that was just horribly taught to my class today (by horribly I mean repugnant) and then this blasted problem was just given to us. It's not in our textbook or any other place I could think to look. And any tips on surviving an Intro to Analysis class with a horrible professor would be nice too.

I recently just bought a wool blend coat with a removal faux fur collar and I would really like to wash it but it says that it's dry clean only. Since this is a wool blend coat, I figured I could just clean it at home instead of taking it to the dry cleaners, but I need a bit of advice for when I choose to wash this at home. I do believe I have a dry cleaning kit but if not I could always go out and get one. Is it also possible to tumble dry low a coat like this?

From the tag in the coat it says that the shell is made of 64% virgin wool and 36% polyester; the body lining is made of 57% acetate and 43% nylon; the sleeve lining is 100% polyester, the rib is 88% acrylic and 12% polyester; the faux fur collar is 70% polyester and 30% acrylic.

This is the coat: http://www.express.com/clothing/wool+blend+faux+fu...

This proof has me stumped. I know that this statement translates to: If 4 divides n^2 then n is even AND if n is even then 4 divides n^2. So I break this up into a 2 case proof where the 1st case is "if 4 divides n^2 then n is even" and the 2nd case is "if n is even then 4 divides n^2".

The 2nd case is easy to prove. It's the 1st case that really has me stuck.

For the 1st case:

Proof by Contradiction: Suppose the statement is false and it's negation is true. So 4 divides n^2 and n is odd. By the definition of divisibility n^2 = 4k, and by the definition of odd, n=2k+1, where k is some integer.

Here's the part where I get stuck. I set n^2=n so,

4k=(2k+1)^2 => 4(k-x^2-x)=1.

What can I conclude from this? Basically how do I finish my contradiction?

I'm a fairly short 19 year-old (5' tall) and I've been searching for these soccer pants in a boy's large and I can't seem to find them. My older sister bought me the men's Sereno soccer pants but those make me look as if I'm wearing MC Hammer's parachute pants. I was just wondering if the Adidas Condivo soccer pants were unisex because the next closest size to fitting me is with the women's.

I recently bought a new laptop and I need to install the TI-Nspire CAS Student Software onto this laptop but whenever I try to activate it, it tells me that my TI-Nspire CAS calculator has already been used to activate the software on my other laptop. So I'm just assuming that it would be possible for me to deactivate the software on my old laptop so that I can activate the one on my new laptop (using the same exact CD and calculator)? I read around and people have been saying that you have to buy a new license even if you're computer had broken, which is utterly ridiculous. I will be attempting to call TI's customer support and I'm most definitely ready for a fairly frustrating answer from them..

Like in honest opinions, put yourself in the perspective of both parties. like I'm 18 and 5'0 tall and it sucks to think about whether or not any girl is going to date you cuz you're so short. So my question is how do you feel about a tall girl dating a short guy? yes i know it can be awkward at times so lets not add that into there. Give me a good explanation of your opinions.

I need help with a final pokemon for my Unova team (no legendaries please). I do plan on using this competitively. I have two pokemon all set (gunna give one the boot) and the rest are the ones I'm planning on using:

Pokemon I have ready:

[Jolly] Emboar Lvl60 (Probably going to stop using it and replace it with Darmanitan)

-EV: 184 Atk | 255 SpA | 59 SpD

-Move 1: Head Smash

-Move 2: Wild Charge

-Move 3: Flamethrower

-Move 4: Arm Thrust <-- will eventually replace

Shiny [Timid] Haxorus Lvl50

-EV: 242 Atk | 254 SpD | 2 Hp (I overdid the EV training for this cept for Hp -_- )

-Move 1: Dual Chop (Will replace eventually)

-Move 2: Dragon Rage (Will replace eventually)

-Move 3: Dragon Claw

-Move 4: Protect

Pokemon I plan to obtain:

[Adamant/Jolly] Darmanitan with a Choice Band?

-Ev: 252 Atk | 4 SDef | 252 Spd (If I don't mess up.lol)

-Move 1: Flare Blitz

-Move 2: Rock Slide

-Move 3: Earthquake?

-Move 4: U-Turn

[Adamant] Samurott with Swimming Goggles?

-EV: 252 SpA | 252 Spd | 4 Hp

-Move 1: Hydro Pump

-Move 2: Blizzard

-Move 3: Grass Knot

-Move 4: Surf

[Timid] Galvantula with Life Orb

-EV: 252 SpA | 252 Spd | 4 Hp

-Move 1: Thunder

-Move 2: Bug Buzz

-Move 3: Volt Switch

-Move 4: Hidden Power Ice (How do you find this move?)

[Timid/Adamant] Hydreigon with Choice Scarf

-EV: 252 SpA | 252 Spd | 4 Hp (Like all the rest.lmao)

-Move 1: Surf

-Move 2: Draco Meteor

-Move 3: Flamethrower?

-Move 4: U-Turn (If I manage to get another one)

My overall pokemon team will consist of Samurott, Darmanitan, Haxorus, Galvantula, Hydreigon. But now I'm stuck on what pokemon will help me finish this set.