What would be the result of 354+true? What is the result of true+true? What is the result of false-true? What is the result of true^3? What is the squareroot of true? Does it make any sense? Is it well defined?
In C, any non-zero int value is synonymous with true and the int value 0 is synonymous with false. So, 354+true is something besides 354; true+true is the sum of two non-zero int values; false-true is simply the arithmetic negation of some non-zero int value; true^3 is some non-zero int value multiplied by itself twice; sqrt(true) is some non-zero int value cast into a double and given to sqrt. It does not have to make sense because these operations are well-defined.
Strongly typed languages usually make type conversions explicit and enforce type restrictions; whereas weakly typed languages usually allow implicit type conversions and relax type restrictions.
Explicit type conversions disallow a value of type T to be treated as a value of type S without invoking a function that takes a value of type T and returns a corresponding value of type S. For example, a conversion from an integer type to a floating point type requires the invocation of a function that performs the conversion. Contrast this with implicit type conversions where a value can be treated as almost any type depending on how it is to be used.
Type restrictions only allow certain operations to be done to certain types. For example, numerical addition mïay only be performed on numerical types. A lack of type restrictions allow for numerical addition to apply for, say, booleans, for example.
A web developer or a functional programmer wouldn't stand a chance here as normal programming only in rare cases involves advanced algoritms like maximum bipartite matchings, maximul flow or other graph related algorithms.
Functional programmers will stand a better chance in these competitions. It is arguably easier to implement graph algorithms in functional programming languages than in imperative programming languages. There are proportionally more functional programmers who have a firm grasp of algorithm design and implementation than programmers who have not used functional programming languages.
Forbidding competition among providers of services is bad everywhere. User fees for road tolls and taxes as well as public schools are bad if private entities are not allowed to respectively provide access to their own privately owned roads and private schools. Moreover, these court records can be distributed by private individuals without incurring any additional costs to the federal government.
Self-enforcing protocol participants do not require the level of trust that are required of impartial middle-men. One way of looking at self-enforcing protocols is to think of the protocol itself as serving the role of a middle-man. The protocol can be scrutinized more thoroughly than any self-serving middle-man and a higher level of trust can be placed on the protocol.
If the courts do rule in favor of the defendant, then they should also rule that the statement in question is true. In this case, the courts should rule that the plaintiff does think that sleeping in moldy apartments is okay.
There should be consequences for plaintiffs who lose libel cases.
Light-dependent reactions in photosynthetic organisms involve light causing a transfer of electrons from chlorophyll molecules to the electron transport chain. Since electricity is simply energy in the form of charged particles, the transfer of electrons involved in photosynthesis is one way that nature uses photosynthesis to create electricity.
MUAD'DIB: the adapted kangaroo mouse of Arrakis, a creature associated in the Fremen earth-spirit mythology with a design visible on the planet's second moon. This creature is admired by Fremen for its ability to survive in the open desert. [1]
Under this same limitation in the SDK license, a Turing machine simulator and a Wolfram rule 110 automaton program will both violate the license because they can run arbitrary code.
I only stated what is sufficient for a game to be acceptable. I never implied that every participant of a war must be dead in order for an acceptable game to be made about it.
Here are counts of the number of primes with a given leading digit. For each radix, I counted the primes up to the radix to the power of 6, so for radix 2, I considered the primes up to 2^6=64, and for radix 10, I considered the primes up to 10^6=1000000. The pairs in each list consist of the leading digit and the number of primes with that leading digit.
It should be (60e6 * 1e3 kcal) / (2*c^2) = 1.39659835 since the normal matter that will also be annihilated will contribute to the mass-energy conversion.
If a prime number is defined to be any integer that is either equal to $0$ or $1$, then every theorem that deals with integers, $p>1$ such that if there exists positive integers $a,b$ such that $p = a b$, then $a=1$ or $b=1$, will still be perfectly valid.
Definitions are essentially shorthands for saying something that would expand textbooks by a considerable amount. Axioms are true statements within a theory. Here are some examples:
Definition. A prime number is an integer $p > 1$ such that if there exists positive integers $a,b$ such that $p = a b$, then $a=1$ or $b=1$.
Axiom. If a subset $K$ of the natural numbers contains $0$ and if a natural number $n \in K$ and the proposition $S(n)$ being true implies $n + 1 \in K$ then $K$ contains all natural numbers.
If one were to use an theory such as Peano arithmetic with the construction of the integers, then the definition of prime numbers makes no statement. It is entirely valid to negate the definition by saying that a prime number is not what was defined and still every theorem in the theory will be valid.
If one were to negate the axiom of mathematical induction within the theory of Peano arithmetic then conceivably either many theorems will be invalid or the entire theory will be inconsistent.
Slashdot Mirror
Here is a high resolution image from the article: http://www.esa.int/images/FIRST_LIGHT_SURVEY.jpg
Here is a high resolution image from the WMAP data: http://upload.wikimedia.org/wikipedia/commons/e/e2/WMAP_2008_94GHz.png
Enjoy.
They did that already. The first crop was lost because the cows could not accept an existence without suffering.
I mean what's next? Engineer ourselves to not feel pain? Then is it OK to murder?
We should engineer ourselves to not feel guilt.
CAN != Should Not
What would be the result of 354+true? What is the result of true+true? What is the result of false-true? What is the result of true^3? What is the squareroot of true? Does it make any sense? Is it well defined?
In C, any non-zero int value is synonymous with true and the int value 0 is synonymous with false. So, 354+true is something besides 354; true+true is the sum of two non-zero int values; false-true is simply the arithmetic negation of some non-zero int value; true^3 is some non-zero int value multiplied by itself twice; sqrt(true) is some non-zero int value cast into a double and given to sqrt. It does not have to make sense because these operations are well-defined.
Strongly typed languages usually make type conversions explicit and enforce type restrictions; whereas weakly typed languages usually allow implicit type conversions and relax type restrictions.
Explicit type conversions disallow a value of type T to be treated as a value of type S without invoking a function that takes a value of type T and returns a corresponding value of type S. For example, a conversion from an integer type to a floating point type requires the invocation of a function that performs the conversion. Contrast this with implicit type conversions where a value can be treated as almost any type depending on how it is to be used.
Type restrictions only allow certain operations to be done to certain types. For example, numerical addition mïay only be performed on numerical types. A lack of type restrictions allow for numerical addition to apply for, say, booleans, for example.
A web developer or a functional programmer wouldn't stand a chance here as normal programming only in rare cases involves advanced algoritms like maximum bipartite matchings, maximul flow or other graph related algorithms.
Functional programmers will stand a better chance in these competitions. It is arguably easier to implement graph algorithms in functional programming languages than in imperative programming languages. There are proportionally more functional programmers who have a firm grasp of algorithm design and implementation than programmers who have not used functional programming languages.
Forbidding competition among providers of services is bad everywhere. User fees for road tolls and taxes as well as public schools are bad if private entities are not allowed to respectively provide access to their own privately owned roads and private schools. Moreover, these court records can be distributed by private individuals without incurring any additional costs to the federal government.
You just made a converse error.
Self-enforcing protocol participants do not require the level of trust that are required of impartial middle-men. One way of looking at self-enforcing protocols is to think of the protocol itself as serving the role of a middle-man. The protocol can be scrutinized more thoroughly than any self-serving middle-man and a higher level of trust can be placed on the protocol.
If the courts do rule in favor of the defendant, then they should also rule that the statement in question is true. In this case, the courts should rule that the plaintiff does think that sleeping in moldy apartments is okay.
There should be consequences for plaintiffs who lose libel cases.
Light-dependent reactions in photosynthetic organisms involve light causing a transfer of electrons from chlorophyll molecules to the electron transport chain. Since electricity is simply energy in the form of charged particles, the transfer of electrons involved in photosynthesis is one way that nature uses photosynthesis to create electricity.
MUAD'DIB: the adapted kangaroo mouse of Arrakis, a creature associated in the Fremen earth-spirit mythology with a design visible on the planet's second moon. This creature is admired by Fremen for its ability to survive in the open desert. [1]
[1] Herbert, Frank. Dune. 1965.
Under this same limitation in the SDK license, a Turing machine simulator and a Wolfram rule 110 automaton program will both violate the license because they can run arbitrary code.
I only stated what is sufficient for a game to be acceptable. I never implied that every participant of a war must be dead in order for an acceptable game to be made about it.
... where every single person who participated in it is dead.
Here are counts of the number of primes with a given leading digit. For each radix, I counted the primes up to
the radix to the power of 6, so for radix 2, I considered the primes up to 2^6=64, and for radix 10, I considered the primes up to 10^6=1000000. The pairs in each list consist of the leading digit and the number of primes with that leading digit.
radix 2
[(1,18)]
radix 3
[(1,66),(2,63)]
radix 4
[(1,200),(2,186),(3,178)]
radix 5
[(1,488),(2,460),(3,441),(4,432)]
radix 6
[(1,1043),(2,994),(3,942),(4,934),(5,908)]
radix 7
[(1,2020),(2,1906),(3,1850),(4,1805),(5,1773),(6,1744)]
radix 8
[(1,3584),(2,3424),(3,3324),(4,3239),(5,3196),(6,3148),(7,3085)]
radix 9
[(1,6009),(2,5735),(3,5588),(4,5455),(5,5410),(6,5263),(7,5254),(8,5220)]
radix 10
[(1,9585),(2,9142),(3,8960),(4,8747),(5,8615),(6,8458),(7,8435),(8,8326),(9,8230)]]
You can watch the machine play classic Pong with xscreensaver's Pong screen saver. http://www.jwz.org/xscreensaver/screenshots/
It should be (60e6 * 1e3 kcal) / (2*c^2) = 1.39659835 since the normal matter that will also be annihilated will contribute to the mass-energy conversion.
The "elementary arithmetic" (Peano arithmetic) is recursive.
We could also use artificial Lunar and Martian magnetospheres to deflect charged particles from approaching the Moon or Mars respectively.
It is unfortunate that no living person may have his or her face printed on currency. We need Donald Knuth alive more than we need him dead.
You seem to not understand the notion of notation or believe that mathematics is based solely on notation.
If a prime number is defined to be any integer that is either equal to $0$ or $1$, then every theorem that deals with integers, $p>1$ such that if there exists positive integers $a,b$ such that $p = a b$, then $a=1$ or $b=1$, will still be perfectly valid.
Definitions are essentially shorthands for saying something that would expand textbooks by a considerable amount. Axioms are true statements within a theory. Here are some examples:
Definition.
A prime number is an integer $p > 1$ such that if there exists positive integers $a,b$ such that $p = a b$, then $a=1$ or $b=1$.
Axiom.
If a subset $K$ of the natural numbers contains $0$ and if a natural number $n \in K$ and the proposition $S(n)$ being true implies $n + 1 \in K$ then $K$ contains all natural numbers.
If one were to use an theory such as Peano arithmetic with the construction of the integers, then the definition of prime numbers makes no statement. It is entirely valid to negate the definition by saying that a prime number is not what was defined and still every theorem in the theory will be valid.
If one were to negate the axiom of mathematical induction within the theory of Peano arithmetic then conceivably either many theorems will be invalid or the entire theory will be inconsistent.