what is a function? just a simple question. who can answer?

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- anonymous

what is a function? just a simple question. who can answer?

- jamiebookeater

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- amistre64

a function is defined as for any one input; there is only one output that can be produced

- amistre64

a relation exists between any given sets of data; but a function is useful in that we can use it to predict events

- anonymous

ahaa tnx

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## More answers

- anonymous

Let A and B be sets of numbers. A function f is a rule that assigns each element of A to a unique element of B.

- anonymous

what if B has infinitely many element from A ., is that can be called as a function?

- amistre64

If A results in many B's then a relation exists; but not a function

- amistre64

If B results from multiple A's, then a function can be determined to best match the results

- anonymous

*an

- anonymous

how is it done?

- anonymous

give all the functions.
A={1,2,3} B={d,f}

- anonymous

There are infinitely many.

- anonymous

prove it.

- amistre64

are you mapping A into B?

- amistre64

f:A -> B

- anonymous

f:A->B

- anonymous

Let A={x: x=1,2 or 3} and B={d or f}. Then\[f:A \rightarrow B \] where f can be any function.

- anonymous

Can you show it for me all the functions?

- anonymous

No. And here are some corrections: B={g(x): g(x)=d or f} and g: A -> B.

- anonymous

Suppose that the set C containing all g such that g: x -> g(x) (where x is in A and g(x) is in B) is finite.
Then there exists a h in C such that h: x -> h(x), where h(x) is in B. But h1= h(x)+1-1 is also in C, and so is h2=h1+1-1, and so is h3=h2+1-1, . . .
Therefore, C is infinite. This is a contradiction.
Therefore, C must be infinite.

- anonymous

And therefore there are infinitely many g.

- anonymous

No: wait. I have made an error. Two function are the same if their domains (A in this case), codomains (B), and effects are the same. Thus h=h1=h2= . . .
However, I still cannot list all functions g by the same argument as in the above comment. Can you see why?

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