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The way I remember it is that when you get a flu shot your entire body doesn't turn into a giant flu virus, because the needle is smaller than your arm is. Then you can easily remember surjection as "the other one". Another one is that in-jections are in-ferior and su-rjections are su-perior.


Take a look at this picture: http://en.wikipedia.org/wiki/File:Surjection.svg This function is NOT injection, because two arrows point into single point in that picture. Now imagine injections at the doctor. Injections usually hurt and you, sure as hell, woudln't want anyone to stick that injection into the same point on your body multiple times. So ...


The best way to remember is to only remember one, then by elimination you know the other. I choose to remember injective as follows: Injections cure things, and you have one injection for one cure. I.e. one to one.


An injection $A \to B$ maps $A$ into $B$, i.e. it allows you to find a copy of $A$ inside $B$. A surjection $A \to B$ maps $A$ over $B$, in the sense that the image covers the whole of $B$. The syllable "sur" has latin origin, and means "over" or "above", as for example in the word "surplus" or "survey".


An injection $A\to B$ provides a correspondence between $A$ and some subset of $B$ -- that, is an INjection points to a copy of $A$ INside $B$.

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