How to show is one-to-one?
How to show , is one-to-one?
I'm quite sure the function is one-to-one as 0 is not an element of the domain, so is not a concern. However doing something like setting where m,v are arbitrary elements of the domain doesn't really work, since n! doesn't have an inverse.
I was able to get something working algebraically by also doing , but I'm quite sure it is circular to do something like that.
Any nudge in the right direction would be greatly appreciated.