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hello welcome to the introduction to bruce video for injections surjections and bijections my name is professor michael polyuk the learning objectives for this video are by the end of this video you should be able to check that a function is one to one or onto and produce counter examples when it isnamp;#39;t and you should be able to get multiple equivalent definitions of injection and surjection we have two pieces of motivation for this one is that injections are special types of functions that donamp;#39;t have any compression and weamp;#39;re going to explain what that means as we go on but itamp;#39;s the the basic idea is that injections are going to preserve a lot of stuff and itamp;#39;s not going to compress anything injections for us will also be the exactly the type of functions that have inverse functions and those are things that we care about another bit of motivation for later on in the course is that injections will be used for formally measuring how many elements