The Mean Thread

[Dixon Carter Lee]

The Literotica Playground is a tea party with your Grandmother and her Church group who are all dead but still manage to show up for Wednesday Night Bingo smelling of toilet water and leaves.

 

[RawHumor]

Damn, I thought this thread was about averages.

 

[sunstruck]

My grandmother is here???

Ahhhhhh!!!!!

 

[Lasher]

In the following I'll consider sets of positive real numbers a1, ..., aN, N a positive integer. Arithmetic mean of the given numbers is defined as

(a1+ ...+aN)/N

whereas their geometric mean is given by

(a1· ... ·aN)1/N

The two quantities are always related in the following way

(a1 + ... + aN)/N(a1· ... ·aN)1/N

Here I am not going to prove the well known inequality but just emphasize a fact that was used by Cauchy in his proof. Namely, if the inequality holds for all N = 2n then it holds for all N 1. This would afford another example of a general proposition implied by its special case.

Thus, assume the inequality holds for all N = 2n and let N = 2n+m, where 0<m<2n and n>0. For i = N+1, ..., 2n+1, define the "missing" a's as

ai = (a1 + ... + aN)/N

Since the inequality holds for N = 2n+1 we have

(a1 + ... + a2n+1)/2n+1(a1· ... ·a2n+1)1/2n+1

Substituting ai=(a1 + ... + aN)/N for i=N+1, ..., 2n+1 results in

(a1 + ... + aN + (2n+1-N)(a1+ ... + aN))/N)/2n+1 (a1· ... ·aN)1/2n+1((a1 + ... + aN)/N)(2n+1-N)/2n+1

Adding similar terms on the left we get

(N+2n+1-N)(a1 + ... + aN)/(N·2n+1)= (a1 + ... + aN)/N

which actually says that the arithmetic mean has not been changed by addition of new terms.

(a1 + ... + aN)/N (a1· ... ·aN)1/2n+1((a1 + ... + aN)/N)(2n+1-N)/2n+1

Dividing by the rightmost term and with one more step to go

((a1 + ... + aN)/N)(1-(2n+1-N)/2n+1) (a1· ... ·aN)1/2n+1
or

((a1 + ... + aN)/N)(N/2n+1) (a1· ... ·aN)1/2n+1

Now raising both sides to the power of 2n+1/N we finally get

(a1 + ... + aN)/N (a1· ... ·aN)1/N

 

[Wiggles]

Did she bring her Vodka?

 

[Dixon Carter Lee]

I saw a woman in her car with what looked like a rat on her lap, but it turned out it was a breed of dog that nautral selection should have relegated to cougar-food a long time ago. I'm telling you, these useless rich women and their rat-pets are fucking with Evolution.

 

[BgMma]

You have all seen them. The cars on the side of the road, up on a jack. Someone is either changing the tire, or doing some sort of doodly shit underneath.

I am the asshole who wants to drive up really fast and knock the jack out from under the car.













Forgive me, my antidepressants have run out.

 

[bluemuse]

Where is the love?

 

[amelia]

Now raising both sides to the power of 2n+1/N we finally get

(a1 + ... + aN)/N (a1· ... ·aN)1/N

holy freaking headache, batman!

 

[BgMma]

Where is the love?

Running down my inner thigh.

 

[Guest]

 

[Lasher]

holy freaking headache, batman!

Pretty mean, huh?

 

[Dixon Carter Lee]

Theme parks are Satan's answer to Real parks.

 

[Zombie Cat]

You want a fiver for WHAT????

Fuck off!

 

[Guest]

What kind of leaves?

 

[Spinaroonie]

This thread has it all, mean spritied attacks, statistical math, insults


5

 

[Dixon Carter Lee]

Anyone who puts "Evil Dead 2" or "Beaches" on their List of the 10 Best Films of All Time should be "clockwork oranged" by Fellini.

 

[bluemuse]

I just love when it rains in SoCAL. The distant sound of screetching tires, crunching metal and breaking glass.......

 

[BgMma]

I just love when it rains in SoCAL. The distant sound of screetching tires, crunching metal and breaking glass.......

Ah, memories.........

 

[sunstruck]

So I was probably the only one turned on by Lasher's post right?

I seriously need to seek help.

 

[Rambrat]

So I was probably the only one turned on by Lasher's post right?

I seriously need to seek help.

I've been trying to tell you that...

 

[Lancecastor]

I seriously need to seek help.

You need a long train ride just to get back to Seeking Help.

 

[seXieleXie]

every person in every one of my classes, excluding me of course, is a complete idiot and a total waste of space.

 

[Problem Child]

The guy running the drive-up at Arby's tonight should be used for medical experimentation, specifically in the area of human pain tolerance.

 

[Dixon Carter Lee]

If I have to read one more indulgent, illiterate sour-grapes inspired screenplay about a couple of 30-something screenwriters in Hollywood chasing their pure cinematic dreams while fighting against the cold cruel Hollywood system, I'm going to firebomb the Writer's Guild.