Other than minimal thought, I have not worked on my previous problem of having a number (not necessarily prime) but who's decimal expansion is made up of only primes.
3/4 is an example. It is a Rational Number, 0.75, but it's digits are all prime.
2/3 is not an example, it a a Rational Number, 0.6666... but none of the digits are prime.
We can construct Integers, Rational, Irrationals, Primes, etc, but is there a way to construct what I will call "prime expansions" for now?
More later as some part of my Gray cell collection works on it.
Tuesday, February 17, 2009
Saturday, February 14, 2009
Moderate Muslims?
Muzzammil Hassan started a cable TV network after 9/11 in New York state to prove to America that American Muslims are a moderate, peaceful people. Today he is charged with killing his wife, Aasiya, by beheading after she served him with divorce papers and a restraining order. Blogger Debbie Schlussel wonders why Hassan has only been charged with second-degree murder. "It's not that easy to behead someone, and it was likely planned in advance 'with malice aforethought,'" she writes.
Schlussel notes that such killings are not rare among Muslims. Known as honor killings, they are typically directed by a male head of household against his spouse or other female family members for violating the honor of their family.
From http://advanceindiana.blogspot.com/2009/02/moderate-american-muslim-tv-executive.html
Schlussel notes that such killings are not rare among Muslims. Known as honor killings, they are typically directed by a male head of household against his spouse or other female family members for violating the honor of their family.
From http://advanceindiana.blogspot.com/2009/02/moderate-american-muslim-tv-executive.html
Friday, February 13, 2009
Numbers
Teaching the Real Number line is fascinating. How dense is it? Are there any holes?
I start off teaching the Natural or Counting numbers. These are easy. They are the numbers you naturally count with, 1, 2, 3, ... where the ... means keeps going to infinity. We can also have the opposites of these, the negative counting numbers,-1, -2, -3, ... off to negative infinity. We can also add in the number 0. It turns out 0,1,2,3... has a special namec alled the Whole Numbers. And if we take the whole numbers and negative counting numbers we get the Integers. So, now we have a nice set of numbers called the Integers that looks like
...-3,2,1,0,1,2,3...
But what's between 0 and 1? 1/2 or 0.5; 2/3 or 0.666... are examples. And, as before, their opposites or the negatives of these. So we can really pack them in. The Integers and all the stuff in between the integers.
The problem is numbers like 1/2, 3/4, 2/3 are very well behaved. They act rationally. As a matter of fact, they are called Rational Numbers. By definition, the Rational Numbers are numbers of the form p/q where p and q are Integers and q cannot be zero.What throws alot of people is that 5, for example, is a Rational Number because 5=5/1 and so fits the definition. An interesting property of the Rational Numbers is that their decimal versions either Terminate (3/4=.75) or Repeat (2/3=.666...)
So our Number line is filling up with the Integers and these things called Rational Numbers between the Integers (and actually including the Integers - as seen before 5=5/1)
What else is there? What about numbers whose decimal expansion do not repeat and do not terminate. For example, 3.1415926536897... These have a name also. They are the Irrational Numbers.
So finally, once we put in the Integers, Rational and Irrational numbers we end up with a verydense set of numbers, the Real Numbers that make up the Real Number line:
As an example ...-3,-2,-1,0,0.5,0.666..., 0.75,1,2,3,3.14159...,3.5,4... Hopefully you get the picture. Between any two numbers, Integer, Rational or Irrational, are more numbers.
There is an Infinite number of Integers
There is an Infinite number of numbers between any two numbers
There is an infinite number of even numbers {2,4,6,...}
There is an Infinite number of odd numbers {1,3,5,7...}
There are even special numbers called prime numbers divisible only by 1 and themseleves:{2,3,5,7,11,13,17...}
There is an infinite number of primes also.
Are we missing any numbers? or are we as dense as can be? Any holes?
You think about it.
Oh, one last thing. Are there any numbers whose digits are all primes? There must be beut how can we construct them?
I start off teaching the Natural or Counting numbers. These are easy. They are the numbers you naturally count with, 1, 2, 3, ... where the ... means keeps going to infinity. We can also have the opposites of these, the negative counting numbers,-1, -2, -3, ... off to negative infinity. We can also add in the number 0. It turns out 0,1,2,3... has a special namec alled the Whole Numbers. And if we take the whole numbers and negative counting numbers we get the Integers. So, now we have a nice set of numbers called the Integers that looks like
...-3,2,1,0,1,2,3...
But what's between 0 and 1? 1/2 or 0.5; 2/3 or 0.666... are examples. And, as before, their opposites or the negatives of these. So we can really pack them in. The Integers and all the stuff in between the integers.
The problem is numbers like 1/2, 3/4, 2/3 are very well behaved. They act rationally. As a matter of fact, they are called Rational Numbers. By definition, the Rational Numbers are numbers of the form p/q where p and q are Integers and q cannot be zero.What throws alot of people is that 5, for example, is a Rational Number because 5=5/1 and so fits the definition. An interesting property of the Rational Numbers is that their decimal versions either Terminate (3/4=.75) or Repeat (2/3=.666...)
So our Number line is filling up with the Integers and these things called Rational Numbers between the Integers (and actually including the Integers - as seen before 5=5/1)
What else is there? What about numbers whose decimal expansion do not repeat and do not terminate. For example, 3.1415926536897... These have a name also. They are the Irrational Numbers.
So finally, once we put in the Integers, Rational and Irrational numbers we end up with a verydense set of numbers, the Real Numbers that make up the Real Number line:
As an example ...-3,-2,-1,0,0.5,0.666..., 0.75,1,2,3,3.14159...,3.5,4... Hopefully you get the picture. Between any two numbers, Integer, Rational or Irrational, are more numbers.
There is an Infinite number of Integers
There is an Infinite number of numbers between any two numbers
There is an infinite number of even numbers {2,4,6,...}
There is an Infinite number of odd numbers {1,3,5,7...}
There are even special numbers called prime numbers divisible only by 1 and themseleves:{2,3,5,7,11,13,17...}
There is an infinite number of primes also.
Are we missing any numbers? or are we as dense as can be? Any holes?
You think about it.
Oh, one last thing. Are there any numbers whose digits are all primes? There must be beut how can we construct them?
Tuesday, February 3, 2009
A horse of a different color
So the US will get rid of GITMO and not engage in torture but they will allow RENDITION. What this means is that we can send suspected terrorists to countries that do believe in torture. So how is this different from the US just doing it? Got me.
Ask yourself a question.
If your child was being held by terrorists, and they knew where they were, wouldn't you do anything to get back your child? This includes torture to extract the information on the whereabouts of your child? (maybe you would just talk to the terrorist or wait for the Judicial system to do their job -- I'm sorry but your child would be dead in the six months it takes to go to trial.
This scenario is no different than the "child" being the US and its citizens.
Let the pro's do their job.
Ask yourself a question.
If your child was being held by terrorists, and they knew where they were, wouldn't you do anything to get back your child? This includes torture to extract the information on the whereabouts of your child? (maybe you would just talk to the terrorist or wait for the Judicial system to do their job -- I'm sorry but your child would be dead in the six months it takes to go to trial.
This scenario is no different than the "child" being the US and its citizens.
Let the pro's do their job.
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