Bacon - Nuff' Said...

zserf on This always bugged me.

2012-02-06T08:29:38.759994-07:00-0700

>You might belong in Hufflepuff Where they are just and loyal Those patient Hufflepuffs are true and unafraid of toil. -The Sorting Hat

Unbelievably lucky huntsman headshot

Sun, 05 Feb 2012 23:54:05 -0700

submitted by zserf to tf2
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A monotonic continuous function that is differentiable nowhere?

Sun, 05 Feb 2012 14:16:10 -0700

Edit: is the LaTex working for others? It isn't for me.

While discussing a theorem my math class started to wonder whether or not it is possible for there to be a monotonic function that is differentiable nowhere. Now, I came up with a function that I thought would be monotonic, continuous, and nowhere differentiable.

[; f=\sum {k=0}^{\infty}f{k}
;]

With each [; f_{k}:\left( \left[ 0,1\right] ,\mathbb{R} \right) ;] being defined as

[; f_{k}\left( x\right)=\dfrac {2ix} {2^{k}\left( 2^{k}+1\right) }-\dfrac {\left( i-1\right) \left( i\right) } {2^{2k}\left( 2^{k}+1\right) }
;]

and the i chosen so that it satisfies the inequality

[; \dfrac {i-1} {2^{k}} \leq x \leq \dfrac {i} {2^{k}}
;]

You can check that each [; f_{k} ;] is continuous by setting [; x=\dfrac{i}{2^k} ;] and showing that you get the same answer whether you choose i or i+1.

Each [; f_{k} ;] is monotonic because the slope is always positive.

and f should not be differentiable at any point of the form [; \dfrac{j}{2^k} ;].

All sounds good. Except, there is a line in my book that says "Using Lebesgue's monotone differentiation theorem (monotonicity implies differentiability almost everywhere)..."

So, my question is,
(i) is f truly a monotonic continuous function? (I'm fairly certain it is)
(ii) is f differentiable anywhere? I know it's not differentiable at j/2^k for any j,k that are natural numbers. I feel like it ought not to be diffirentiable, but I can conceive that it may be at points such as 1/3.

submitted by zserf to math
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My Little Pony & TF2

Sat, 04 Feb 2012 20:36:26 -0700

submitted by zserf to tf2
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zserf on What are some of the lesser known reddits that you wish were more populated?

2012-02-04T12:19:34.592654-07:00-0700

[/r/juggling](http://www.reddit.com/r/juggling)

zserf on Chinese is hardcore

2012-02-02T21:51:52.253172-07:00-0700

Shi is pronounced more closely to sure than shit.

zserf on What popular quote do you hate with a passion?

2012-02-02T13:31:42.817857-07:00-0700

[relevant Cy&H](http://www.explosm.net/comics/1841/)

zserf on Is this an accurate definition of a definite integral?

2012-01-31T23:38:14.520492-07:00-0700

Yeah, you can think of it as for (i=n;i<=k;i++){ sum=sum+f(i); where i=n is below sigma, and k is the number above, with f being the function to the right of sigma.

zserf on Is this an accurate definition of a definite integral?

2012-01-31T23:30:14.953118-07:00-0700

You add 1 each time to i though. You have no idea if b-a/delta(x) is an integer, and if it's not, the sigma makes no sense.

zserf on I'm a programmer that stumbled across an interesting fractal. Can anyone shed some light on what I've done?

2012-01-31T21:21:56.879139-07:00-0700

You will get fractals like this if you do anything in the correct range. Anything larger than 1/2 gets you overlapping triangles, and anything smaller than 2/3 gets you empty space. It just so happens that phi is in the right range to have both of these properties be easily observable. Values between .6 and .63 look the best to me. I'm having trouble with imgur, but if you have java you can play around with this code, which goes quite quickly. public class Serpenski{ public static void main(String[] args){ double x=Double.parseDouble (args [0]); double y=Double.parseDouble (args [1]); double a=Double.parseDouble (args [2]); double b=Double.parseDouble (args [3]); double point1x=0; double point1y=0; double point2x=1; double point2y=0; double point3x=.5; double point3y=.86603; StdDraw.setXscale(0.0, 1.0); StdDraw.setYscale(0.0, 1.0); StdDraw.show (0); for (double i=1.0; i<=100000; i++){ double r=Math.random(); if (r<(.333)){ StdDraw.point(((a*point1x+b*x)/(a+b)),((a*point1y+b*y)/(a+b))); x=(a*point1x+b*x)/(a+b); y=(a*point1y+b*y)/(a+b); } else if (r<(.667)){ StdDraw.point(((a*point2x+b*x)/(a+b)),((a*point2y+b*y)/(a+b))); x=(a*point2x+b*x)/(a+b); y=(a*point2y+b*y)/(a+b);} else { StdDraw.point(((a*point3x+b*x)/(a+b)),((a*point3y+b*y)/(a+b))); x=(a*point3x+b*x)/(a+b); y=(a*point3y+b*y)/(a+b);} } StdDraw.show (0); } } Change all the &lt to < . I'm not sure why reddit is switching that.

zserf on Ever heard of the Baader-Meinhof phenomenon? You probably will soon! What's your craziest experience with this phenomenon, Reddit?

2012-01-30T22:41:34.740749-07:00-0700

In my Data Structures and Algorithms class we gave an example about mathematical induction and successor functions. The next day in Mathematical Logic a different teacher gave nearly an identical example. It's odd, because both of these topics were tangents.

zserf on TIL that the incarceration rate in the USA is the highest in the world, and that the incarceration rate of its black population exceeds that of South Africa at the height of apartheid.

2012-01-30T22:12:43.726115-07:00-0700

>"As one might expect, a good case can be made that fewer Americans are now being victimized" thanks to the tougher crime policies, Paul Cassell, an authority on sentencing and a former federal judge, wrote in The Stanford Law Review. I would say a good case can also be made that sending people to prison for recreational drug use and minor offenses is a form of victimization.

zserf on "If an alien force, vastly more powerful than us, landing on Earth and demanding the value of R(5,5) or they will destroy our planet, we should marshal all our computers and mathematicians and attempt to find the value. But if they ask for R(6,6), we should attempt to destroy the aliens."

2012-01-30T22:02:36.341894-07:00-0700

I can confirm this. I've never had a time when I was threatened by a vast alien life force when I wasn't required to show my work.

zserf on TIL the first assassination attempt on a US President happened today in 1835, thwarted by a jammed gun. Andrew Jackson beat the crap out of his failed assassin with the help of (The) Davy Crockett

2012-01-30T12:13:53.288978-07:00-0700

Reading that right now.

zserf on Would You Spend Two Years in Solitary Confinement for $22 million?

2012-01-27T17:30:35.864662-07:00-0700

[INTP subreddit](http://reddit.com/r/intp) I'm also an INTP, and I most certainly would not choose to do it. I don't even know what I'd do with that much money.

85 year old Alaskan women hits moose with shovel repeatedly to keep it from killing her husband

Wed, 25 Jan 2012 17:38:52 -0700

submitted by zserf to alaska
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zserf on Mankind is moving from a type 0 to a type 1 society, all thanks to the internet.

2012-01-25T13:47:08.443396-07:00-0700

[Song about Fermi's Paradox](http://www.youtube.com/watch?v=zqzMAnPKa_s&t=30s).

zserf on Ha! Parents!

2012-01-25T08:08:29.164887-07:00-0700

Enemy of the nighttime

zserf on What article of clothing do you immediately judge a stranger for wearing?

2012-01-24T20:59:48.063559-07:00-0700

If I don't wear sweatpants I get a lot of questions because it is such an anomaly.

zserf on What is the most shameless joke you have ever heard?

2012-01-24T20:29:58.663778-07:00-0700

My mom went to a wedding where the priest said this during the ceremony.

zserf on 10 Misconceptions Debunked

2012-01-24T10:47:36.743833-07:00-0700

Unless they are Athabaskan, Aleut, Eyak, Haida, Tlingit, Tsimshian, Yupik or part of another non-inuit tribe.

zserf on Dear r/math please help me figure out this number puzzle. I can't figure out the pattern

2012-01-23T22:39:58.363762-07:00-0700

>Don't feel badly. [One of my favorite movie quotes...](http://www.imdb.com/title/tt0373469/quotes?qt=qt0397222)

zserf on New Hampshire Senate passes bill that allows defense attorneys to state the right of jury nullification to the jury.

2012-01-23T06:11:24.221469-07:00-0700

Wrong state, that was Iowa. Santorum got 5th in New Hampshire.

How the number of delegates each state gets in the Republican National Convention is decided. Scroll down for a handy table.

Sat, 21 Jan 2012 22:50:27 -0700

submitted by zserf to moderatepolitics
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zserf on Ron Paul finishes last in South Carolina

2012-01-21T19:26:01.221400-07:00-0700

According to Wikipedia, Romney only has 25 delegates before South Carolina, but Huntsman's 2 are almost definitely going to him. Perry's 3 should go to Gingrich According to fivethirtyeight.com, Gingrich is expected to win atleast 5 of the 7 districts, and possibly all 7. If he wins all 7, that would put the totals at **Romney**: 27 **Gingrich**: 27 **Paul**: 10 **Santorum**: 8 The latest polls out of Florida have Romney at 42% and Gingrich at 25%. News out of South Carolina is likely to affect those numbers though. You need 1144 delegates to get the nomination. Edit: There is significant uncertainty as to who will get exactly how many delegates from Iowa. They have several conventions, so keep that in mind. Also, The only candidates on Virginia's ballot are Romney and Ron Paul. As far as I can tell, there are 46 candidates awarded to the winner. Technically, it's proportional unless somebody gets more than 50%, in which case it is winner take all. Seeing as there are only 2 candidates, somebody is going to get a majority.