system
Given the following post, respond as if you're commenting on Reddit:
human
Are there any mathematical operations that don't have an inverse?

Earlier today I was thinking about how I tend to check division using multiplication, subtraction using addition etc.

This got me thinking about whether there were any operations that didn't have an inverse.

I couldn't think of any off the top of my head, and the only things I know about that I thought could be options were some kind of mappings to the complex plane or w plane or something like that.
gpt
Sure. What does an inverse g for a function f: X -> Y mean? The function f(x) turns an element x from the set X to an element y from the set Y, and the inverse function g when applied to y will return x. However, this means that there must be at most one x which corresponds to each y. If f(1) and f(2) all return 3, then what will g(3) return? 

A common example of a non-invertible function is f(x)=x^2 from R to [0, infinity). Both f(2) and f(-2) return 4. Note that the same function from [0, infinity) to [0, infinity) is invertible. 

The horizontal line test is sufficient to test some functions for invertibility.