on·to
                    
                                                                                                              
                                                                                                                                  ˈȯn-(ˌ)tü 
                                                                                                                              
            ˈän-
                                                      
                                                          1
                    
                                          
              
          
                                                      : to a position on                                      
              
                             
We climbed onto the roof.
                                       Turn left onto Fifth Avenue.
                         
                
                    2
                    
                                          
              
          
                                                      : in or into a state of awareness about                                      
              
                             
put me onto your methods
                                       was onto something that should have been pursued further—
Bosley Crowther
                         
                
                    3
                    
                                          
              
            
                  —used as a function word to indicate a set each element of which is the image of at least one element of another set
a function mapping the set S onto the set T
    
                
                    
                                
              
          
                                                      : mapping elements in such a way that every element in one set is the image of at least one element in another set                                      
              
                             
a function that is one-to-one and onto
                         
                
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  Merriam-Webster unabridged




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