Question

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

Answer 1

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

Answer 2

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

Answer 3

ahaa tnx

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

*an

Answer 9

how is it done?

Answer 10

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

Answer 11

There are infinitely many.

Answer 12

prove it.

Answer 13

are you mapping A into B?

Answer 14

f:A -> B

Answer 15

f:A->B

Answer 16

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

Answer 17

Can you show it for me all the functions?

Answer 18

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

Answer 19

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.

Answer 20

And therefore there are infinitely many g.

Answer 21

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?