|
|
Post by abacus9900 on Sept 9, 2010 18:50:20 GMT 1
In maths, what is a function?
|
|
|
|
Post by kiteman on Sept 9, 2010 19:29:58 GMT 1
|
|
|
|
Post by abacus9900 on Sept 9, 2010 20:16:27 GMT 1
Thanks, but why do we need functions? |
|
|
|
Post by kiteman on Sept 9, 2010 21:35:06 GMT 1
They're an easy short-hand. rather than repeatedly writing out a complex algebraic string, you just write f(x). Various functions can also be combined into other formulae, making it possible to write highly-complex equations with only a few characters.
|
|
|
|
Post by lazarus on Sept 10, 2010 2:15:23 GMT 1
They're an easy short-hand. rather than repeatedly writing out a complex algebraic string, you just write f(x). Various functions can also be combined into other formulae, making it possible to write highly-complex equations with only a few characters. They could also be thought of sub routines if you know a little about computer programming - sub routines are actually called functions in some languages like C++. |
|
|
|
Post by Progenitor A on Sept 10, 2010 14:48:59 GMT 1
In maths, what is a function? In my understanding, from the days of maths on my degree course. a function is an OPERATION that works upon an INPUT and produces an OUTPUT that changes the input. |
|
|
|
Post by speakertoanimals on Sept 10, 2010 15:40:30 GMT 1
Well, not a brilliant maths course then if you think it changes the input..........
The basic idea, as others have said, is that the output of a function (which may be a number, a vector, or something more complicated) is totally determined by the input (which again may be a number, a vector, or something more complicated). It is a very basic relationship, and non-symmetric in that knowing the output doesn't necessarily tell you what the input was, but knowing the input tells you the output.
So, think of your bank balance. Your bank balance is a function of:
money you put in
money you take out
bank charges
interest paid
transfers to other accounts
So, knowing all of the above, you can find your balance, but knowing your balance doesn't tell you exactly where that money came from, what proportion of it was payments in, or interest.
strictly speaking in this case, it should be something like the amount in your account at the end of the month is a function of:
starting balance
total payments in
total taken out
total interest paid
bank charges
In terms of relationships between mathematical objects, about the most basic you can imagine.
|
|
|
|
Post by abacus9900 on Sept 10, 2010 15:53:16 GMT 1
Thank you Speaker. I think naymissus was saying the same thing though.
|
|
|
|
Post by oldpythonboy on Sept 10, 2010 22:11:51 GMT 1
In maths, abacuscus, for example f(x)=x^3-3x^2+3x-1 means that for input values of x there are output values for f(x). f is the function name x is the input the function itself x^3-3x^2+3x-1 is what is output an input value of x=1 would give an outut value, f(x), of 0. (The function above is an expansion of f(x)=(x-1)^3) Here's a simple example of a car taking off. What is the speed after 5 seconds with acceleration of 12 miles per second. v=final velocity (the function) u=initial velocity a=acceleration t=time v=u+at In this case u=0, a=12mps/s, t=5 secs v=0+5x12=60mph after 5 secs or 0 to 60 in 5 seconds. BUY THAT CAR!  |
|
|
|
Post by abacus9900 on Sept 11, 2010 10:10:22 GMT 1
In maths, abacuscus, for example f(x)=x^3-3x^2+3x-1 means that for input values of x there are output values for f(x). f is the function name x is the input the function itself x^3-3x^2+3x-1 is what is output an input value of x=1 would give an outut value, f(x), of 0. (The function above is an expansion of f(x)=(x-1)^3) Here's a simple example of a car taking off. What is the speed after 5 seconds with acceleration of 12 miles per second. v=final velocity (the function) u=initial velocity a=acceleration t=time v=u+at In this case u=0, a=12mps, t=5 secs v=0+5x12=60mph after 5 secs or 0 to 60 in 5 seconds. BUY THAT CAR! Thanks, oldpythonboy, good example. So a maths function is really a formula applied to some input that produces some output that gives information that is useful. Magic. |
|
|
|
Post by speakertoanimals on Sept 13, 2010 16:22:09 GMT 1
Thank you Speaker. I think naymissus was saying the same thing though. No, because s/he had the output changing the input, whereas in general, the output can be a totally different beast to the input.Hence a lousy maths course........... I suspect something to do with programming, where in many cases, you generate a new value by calling a function, and replace the input. But that is just programming, which is not the same as maths. Not useful, just sayd that wherever the input lives, or whatever it is, is related in a definite way to the output ,wherever that lives. May or may not be useful, but important to know in many situations, what depends on what. Exactly how something depends on something else, and you end up with functions. |
|
|
|
Post by abacus9900 on Sept 16, 2010 17:02:50 GMT 1
I don't think much of maths would be worthwhile if it didn't do something useful. You're not making a distinction between applied maths and pure maths.
|
|
|
|
Post by speakertoanimals on Sept 16, 2010 19:39:47 GMT 1
Because functions apply in both.
And you obviously don't know much maths if you also think that the only point of maths is that which does something useful.
Most of maths doesn't, and in many cases, that isn't why it was developed in the first place (or discovered, rather, since I'm a platonist).
Sorry to see you have such a low regard for abstract knowledge...........
|
|
|
|
Post by abacus9900 on Sept 17, 2010 10:53:03 GMT 1
Because functions apply in both. And you obviously don't know much maths if you also think that the only point of maths is that which does something useful. Most of maths doesn't, and in many cases, that isn't why it was developed in the first place (or discovered, rather, since I'm a platonist). Sorry to see you have such a low regard for abstract knowledge........... You can't really think that maths is done for its own sake can you? If you do you are very naive. |
|
|
|
Post by eamonnshute on Sept 17, 2010 11:12:07 GMT 1
You can't really think that maths is done for its own sake can you? If you do you are very naive. Nonsense. Why do you think Cantor did his work on transfinite arithmetic? Why do people do mathematical puzzles, such as sudoku, if not for their own sake? Mathematicians do Maths because it is beautiful and because it is interesting - any practical applications are nice, but that is not the motivating factor. I would be just as interested in Maths (and Science) even if it was completely useless. |
|
