This silly example shows me every year that my students do not understand how some functions can act differently from others. This assumption is correct, but when I ask them they cannot even imagine any discontinuous possibility such as a Star Trek beam transporter. Students assume that the distance from my home is a continuous function, so I must at some point be exactly ten miles from my home (school is 22 miles away). This student will get into trouble when this is not the case.Įxample story: when I begin to teach the Intermediate Value Theorem for continuous functions, I give the example of me driving to school from my home. Catastrophe theory, developed in the 1970's, shows there are a variety of ways to get discontinuity, with a variety of applications.Īny student who does not directly think about continuous and discontinuous functions early in his/her math training may assume that all functions are continuous.The study of Chaos, resulting from weather and other such topics, gives results that are practically discontinuous, even if continuous in theory.Schrodinger's equation assumes continuity and differentiability, but in the Copenhagen interpretation of quantum theory any measurement causes a collapse of the waveform and things become discontinuous: the spin is either up or down, etc. Quantum theory is a mixture of the continuous and the discontinuous.Many computer routines produce discontinuous output, even if the data is near-continuous. Computers and their digitization of data.However, more and more discontinuous functions are appearing in the various sciences. Information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you areĮither the copyright owner or a person authorized to act on their behalf.Most functions that are studied by physicists and other scientists are continuous. Your copyright is not authorized by law, or by the copyright owner or such owner’s agent (b) that all of the Your name, address, telephone number and email address andĪ statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe Which specific portion of the question – an image, a link, the text, etc – your complaint refers to Link to the specific question (not just the name of the question) that contains the content and a description of Sufficient detail to permit Varsity Tutors to find and positively identify that content for example we require Please follow these steps to file a notice:Ī physical or electronic signature of the copyright owner or a person authorized to act on their behalf Īn identification of the copyright claimed to have been infringed Ī description of the nature and exact location of the content that you claim to infringe your copyright, in \ On or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Thus, if you are not sure content located Misrepresent that a product or activity is infringing your copyrights. Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially Your Infringement Notice may be forwarded to the party that made the content available or to third parties such Means of the most recent email address, if any, provided by such party to Varsity Tutors. Infringement Notice, it will make a good faith attempt to contact the party that made such content available by If Varsity Tutors takes action in response to Information described below to the designated agent listed below. Or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one ![]() ![]() Have discontinuities, but these discontinuities occur as vertical asymptotes, not holes, and thus are not considered removeable.Īnd are continuous over all the real values of they have no discontinuities of any kind. Therefore, we can say that there is a removeable discontinuty at. ![]() However, if we were to just define, then we could essentially "remove" this discontinuity. What this means is that will look just like the parabola with the equation EXCEPT when, where there will be a hole in the graph. Notice that we could simplify as follows:Īs we can see, the limit of exists at, even though is undefined. Put another way, if there is a removeable discontinuity at, then the limit as approaches exists, but the value of does not.įor example, the function contains a removeable discontinuity at. A removeable discontinuity occurs whenever there is a hole in a graph that could be fixed (or "removed") by filling in a single point.
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