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Need a complete list of functions and thier inverses

  1. Feb 6, 2013 #1
    I can't find this anywhere on google.

    I'm looking for a complete list of functions and their inverses.
    Here's a partial list as an example
    *, /
    +, -
    e^x, ln(x)
    sin(), sin^-1()
    d/dx, ∫
    etc..

    Why isn't there a list of all of them? You would think that some mathematician would find joy in compiling one...
     
  2. jcsd
  3. Feb 6, 2013 #2
    Assuming......just assuming.......that you aren't trolling.

    There are an infinite amount of functions, and I'm going to take a gander and say that the vast majority of them do not have inverses.

    There are, however, a relativity short list of 'common' functions, and I'm sure it is very easy to google a list of their inverses, though you've listed a number already.

    I'll stress here that neither ##\frac{d}{dx}## nor ##\int## are functions, though they are inverse operations.
    Nor are multiplication, division, addition or subtraction, they are all operations.
     
  4. Feb 6, 2013 #3

    micromass

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    There are [itex]2^{2^{\aleph_0}}[/itex] functions from [itex]\mathbb{R}\rightarrow \mathbb{R}[/itex]

    This means that the number of functions from [itex]\mathbb{R}[/itex] to [itex]\mathbb{R}[/itex] is not only infinite, but a number of degrees above the smallest possible infinity.

    Thus, I fear that a complete list of functions would not be very feasible.

    If you want a list of all possible function between all possible sets. Then I'm afraid that they don't even form a set. The number of functions form a proper class. This means that is quite larger than anything mathematics can handle. So a list would be rather impossible.
     
  5. Feb 6, 2013 #4

    micromass

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    I would actually consider all those things as functions...
     
  6. Feb 6, 2013 #5
    ok. then what I'm looking for is a complete list of opposite operations.
     
  7. Feb 6, 2013 #6

    micromass

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    Still too large (= infinity).
     
  8. Feb 6, 2013 #7
    no it's not. There are a few dozen we learn in algebra, another dozen from trig, only 2 from calc (d/dx and ∫ ), diff eq may add more to the list but I didn't notice any. you see? Get real. The question is not that hard. A list of opposite functions would be handy to have when solving for a variable in a complex algebraic equation.
     
  9. Feb 6, 2013 #8

    micromass

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    So, you are saying that there are only a finite number of bijective functions in existence? Do you have any proof/evidence for that?
     
  10. Feb 6, 2013 #9

    micromass

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    Anyway, the OP is just a troll, so I'm locking this.
     
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