Need a complete list of functions and thier inverses

  • #1
179
0
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...
 

Answers and Replies

  • #2
778
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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
22,129
3,297
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.
 
  • #4
22,129
3,297
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.

I would actually consider all those things as functions...
 
  • #5
179
0
Assuming......just assuming.......that you aren't trolling.

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.
ok. then what I'm looking for is a complete list of opposite operations.
 
  • #6
22,129
3,297
ok. then what I'm looking for is a complete list of opposite operations.

Still too large (= infinity).
 
  • #7
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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
22,129
3,297
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

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
22,129
3,297
Anyway, the OP is just a troll, so I'm locking this.
 

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