Swlabr1
				
				
			 
			
	
	
	
		
	
	
			
		
		
			
			
				
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If there exists an injection $f: X\rightarrow Y$ then there `obviously' exists a surjection $g:Y\rightarrow X$, got by noting that the restriction of $f$ to $f(X)$ is a bijection between $X$ and $f(X)$ and so invertible, and then mapping everything else in $Y$ to some fixed element in $X$. However, we have to `choose' this element, and I was wondering if there are any problems in doing this (w.r.t. the axiom of choice)?
If we do have to invoke AOC, is there any way of `inverting' an injection to get a surjection without using AOC?
				
			If we do have to invoke AOC, is there any way of `inverting' an injection to get a surjection without using AOC?
 
 
		 
 
		