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anonymous

  • 5 years ago

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

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  1. amistre64
    • 5 years ago
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    a function is defined as for any one input; there is only one output that can be produced

  2. amistre64
    • 5 years ago
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    a relation exists between any given sets of data; but a function is useful in that we can use it to predict events

  3. anonymous
    • 5 years ago
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    ahaa tnx

  4. anonymous
    • 5 years ago
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    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.

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

  6. amistre64
    • 5 years ago
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    If A results in many B's then a relation exists; but not a function

  7. amistre64
    • 5 years ago
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    If B results from multiple A's, then a function can be determined to best match the results

  8. anonymous
    • 5 years ago
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    *an

  9. anonymous
    • 5 years ago
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    how is it done?

  10. anonymous
    • 5 years ago
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    give all the functions. A={1,2,3} B={d,f}

  11. anonymous
    • 5 years ago
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    There are infinitely many.

  12. anonymous
    • 5 years ago
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    prove it.

  13. amistre64
    • 5 years ago
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    are you mapping A into B?

  14. amistre64
    • 5 years ago
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    f:A -> B

  15. anonymous
    • 5 years ago
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    f:A->B

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

  17. anonymous
    • 5 years ago
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    Can you show it for me all the functions?

  18. anonymous
    • 5 years ago
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    No. And here are some corrections: B={g(x): g(x)=d or f} and g: A -> B.

  19. anonymous
    • 5 years ago
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    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.

  20. anonymous
    • 5 years ago
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    And therefore there are infinitely many g.

  21. anonymous
    • 5 years ago
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    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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