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Why aren’t all functions well-defined? | Gowers's Weblog

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I’m in the happy state of just having finished marking exams for this year. There is very little of interest to say about the week that was removed from my life: it would be fun to talk about particularly bizarre mistakes, but I can’t really do that, especially as the results are not yet known (or even fully decided). However, one general theme emerged that made no difference to anybody’s marks. There seems to be a common misconception amongst many Cambridge undergraduates that I’d like to discuss here in the hope that I can clear things up for a few people. (It is an issue that I have discussed already on my web page, but rather than turning that into a blog post I’m starting again.) The question where the misconception made itself felt was one about functions, injections, surjections, etc. I noticed that a lot of people wrote things like, “If then so is well defined.” Now if you fully understand what a function is, then you will find this quite amusing: if then trivially by the

Why aren&#8217;t all functions well-defined? | Gowers&#039;s Weblog Gowers&#039;s Weblog Mathematics related discussions << Swine flu and British public health policy DHJ write-up and other matters >> Why aren&#8217;t all functions well-defined? I&#8217;m in the happy state of just having finished marking exams for this year. There is very little of interest to say about the week that was removed from my life: it would be fun to talk about particularly bizarre mistakes, but I can&#8217;t really do that, especially as the results are not yet known (or even fully decided). However, one general t

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