# Need a complete list of functions and thier inverses

1. Feb 6, 2013

### Jeff12341234

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. Feb 6, 2013

### Vorde

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.

3. Feb 6, 2013

### micromass

There are $2^{2^{\aleph_0}}$ functions from $\mathbb{R}\rightarrow \mathbb{R}$

This means that the number of functions from $\mathbb{R}$ to $\mathbb{R}$ 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.

4. Feb 6, 2013

### micromass

I would actually consider all those things as functions...

5. Feb 6, 2013

### Jeff12341234

ok. then what I'm looking for is a complete list of opposite operations.

6. Feb 6, 2013

### micromass

Still too large (= infinity).

7. Feb 6, 2013

### Jeff12341234

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.

8. Feb 6, 2013

### micromass

So, you are saying that there are only a finite number of bijective functions in existence? Do you have any proof/evidence for that?

9. Feb 6, 2013

### micromass

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

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