Thank you for taking the time to look at all this and point me towards other ways of looking at it. The real problem I find with googles' answer is it's lack of determinism. As the wikipedia link you posted states:
The "rule" defining a function can be specified by a formula, a relationship, or simply a table listing the outputs against inputs. The most important feature of a function is that it is deterministic, always producing the same output from the same input.
The reason why I believe Google's answer fails to be detrministic is simply because if you change the base, the whole thing falls apart. In other words, it's not a relation between *values* of the domain set (1,2,3,4,5) and the range set. -As you pointed out, I'm keeping with the formal (or as you said "specialized") definition of the term "function" rather than making allowing for a loose and generalized definition.
You could, for example, just compute the cubic polynomial interplant of the four given points, and then compute the fifth point rather easily from the resultant cubic. I haven't done this, but I am pretty sure that that the point you get will be different than your fifth point, or google's fifth point. Nonetheless, all are correct.
It is not my own work but a firend pointed out a problem with your suggested polynomial approach. This is what he had to say:
The first thing I tried was the method of finite differences. In essence use the four given values to solve for a olynomial of the form:
f(n) = a3*x^3 + a2*x^2 + a1*x^1 + a0
Doing this gives f(5) = 2775619300. While finite differences only solves for polynomials, experience and intuition let one recognize other patterns. E.g. I can usually recognize exponentials.
For this to have been valid I would have expected it to yield a quadratic rather than a cubic. That is, I would have expected f(1) through f(3) to predict f(4) via this method.
It seem like we could end up debating the definitions of both "function" and "correct" endlessly.;-)
Have you seen anyone able state the function of google's answer? I've tried a number of times but have not been able to do it. I'm not saying it can not be done but I've had no luck at it.
Though I don't know who you are, I appreciate the time you've taken. If you'd like to contact me via email, please do. I'd love to prove myself wrong and find a somwhat formalized (an exception for decimal only) function for the google answer.
(slashdot formatting...)
I only posted the link to/. to see comments from other people. Believe it or not, I wrote it but that does not matter much.
The link you posted to the definition of a function (on wolfram) supports the claim that google's answer is wrong:
"A function is a relation that uniquely associates members of one set with members of another set."
The "answer" according to google has no relation associating members of one set with members of the other set, so it is not a function. If there is a mathematical relationship then anyone would be able to state the function. I really tried to state the function for google's answer but failed to find a way to do it. If someone has managed to succeed, I'd love to see it.
If one can not state the function, one can not prove there is a relation. Alternately, if one can not state the relation, one can not have a function.
The answer accepted by google is nothing more than blindly searching for the next occurance of something. There is no relation between one occurance and the next (that I've found/proven with their accepted answer), so as far as anyone knows, googles answer is not a function.
Since it is assumed that f is a function, and a true function really does exist that satisfies the given 1 through 4, then the answer said real function gives for 5 is far more correct than a whimsical search for a pattern.
Googles solution is not mathematicly sound. Until I see someone state the google answer as real function and prove the relationship, their answer is at best nonsense numerology.
I only posted the link to/. to see comments from other people. Believe it or not, I wrote it but that does not matter much.
The link you posted to the definition of a function (on wolfram) supports the claim that google's answer is wrong:
"A function is a relation that uniquely associates members of one set with members of another set."
The "answer" according to google has no relation associating members of one set with members of the other set, so it is not a function. If there is a mathematical relationship then anyone would be able to state the function. I really tried to state the function for google's answer but failed to find a way to do it. If someone has managed to succeed, I'd love to see it.
If one can not state the function, one can not prove there is a relation. Alternately, if one can not state the relation, one can not have a function.
The answer accepted by google is nothing more than blindly searching for the next occurance of something. There is no relation between one occurance and the next (that I've found/proven with their accepted answer), so as far as anyone knows, googles answer is not a function.
Since it is assumed that f is a function, and a true function really does exist that satisfies the given 1 through 4, then the answer said real function gives for 5 is far more correct than a whimsical search for a pattern.
Googles solution is not mathematicly sound. Until I see someone state the google answer as real function and prove the relationship, their answer is at best nonsense numerology.
The "function of x" notation used by google does indeed imply a "function" of some sort but the "correct" answer according to google is not a function in spite of it's notation.
Slashdot Mirror
Thank you for taking the time to look at all this and point me towards other ways of looking at it. The real problem I find with googles' answer is it's lack of determinism. As the wikipedia link you posted states:
The reason why I believe Google's answer fails to be detrministic is simply because if you change the base, the whole thing falls apart. In other words, it's not a relation between *values* of the domain set (1,2,3,4,5) and the range set. -As you pointed out, I'm keeping with the formal (or as you said "specialized") definition of the term "function" rather than making allowing for a loose and generalized definition.
It is not my own work but a firend pointed out a problem with your suggested polynomial approach. This is what he had to say:
It seem like we could end up debating the definitions of both "function" and "correct" endlessly.
Have you seen anyone able state the function of google's answer? I've tried a number of times but have not been able to do it. I'm not saying it can not be done but I've had no luck at it.
Though I don't know who you are, I appreciate the time you've taken. If you'd like to contact me via email, please do. I'd love to prove myself wrong and find a somwhat formalized (an exception for decimal only) function for the google answer.
mercury no spam at abac dot com
Thanks, JCR
(slashdot formatting...) /. to see comments from other people. Believe it or not, I wrote it but that does not matter much.
I only posted the link to
The link you posted to the definition of a function (on wolfram) supports the claim that google's answer is wrong:
"A function is a relation that uniquely associates members of one set with members of another set."
The "answer" according to google has no relation associating members of one set with members of the other set, so it is not a function. If there is a mathematical relationship then anyone would be able to state the function. I really tried to state the function for google's answer but failed to find a way to do it. If someone has managed to succeed, I'd love to see it.
If one can not state the function, one can not prove there is a relation. Alternately, if one can not state the relation, one can not have a function.
The answer accepted by google is nothing more than blindly searching for the next occurance of something. There is no relation between one occurance and the next (that I've found/proven with their accepted answer), so as far as anyone knows, googles answer is not a function.
Since it is assumed that f is a function, and a true function really does exist that satisfies the given 1 through 4, then the answer said real function gives for 5 is far more correct than a whimsical search for a pattern.
Googles solution is not mathematicly sound. Until I see someone state the google answer as real function and prove the relationship, their answer is at best nonsense numerology.
I only posted the link to /. to see comments from other people. Believe it or not, I wrote it but that does not matter much.
The link you posted to the definition of a function (on wolfram) supports the claim that google's answer is wrong:
"A function is a relation that uniquely associates members of one set with members of another set."
The "answer" according to google has no relation associating members of one set with members of the other set, so it is not a function. If there is a mathematical relationship then anyone would be able to state the function. I really tried to state the function for google's answer but failed to find a way to do it. If someone has managed to succeed, I'd love to see it.
If one can not state the function, one can not prove there is a relation. Alternately, if one can not state the relation, one can not have a function.
The answer accepted by google is nothing more than blindly searching for the next occurance of something. There is no relation between one occurance and the next (that I've found/proven with their accepted answer), so as far as anyone knows, googles answer is not a function.
Since it is assumed that f is a function, and a true function really does exist that satisfies the given 1 through 4, then the answer said real function gives for 5 is far more correct than a whimsical search for a pattern.
Googles solution is not mathematicly sound. Until I see someone state the google answer as real function and prove the relationship, their answer is at best nonsense numerology.
The "function of x" notation used by google does indeed imply a "function" of some sort but the "correct" answer according to google is not a function in spite of it's notation.
Not that complicated? -It seems you got the wrong answer, so did google.
Oddly enough, there actually is a working f(x) answer and even google does not know what it is...
http://www.datarescue.com/ubb/ultimatebb.php?ubb=