Mathematical Economics I
Mathematical Economics I ECON 703
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This 2 page Study Guide was uploaded by April Jerde on Thursday September 17, 2015. The Study Guide belongs to ECON 703 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 52 views. For similar materials see /class/205166/econ-703-university-of-wisconsin-madison in Economcs at University of Wisconsin - Madison.
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Date Created: 09/17/15
GUIDELINES ON WRITING PROOFS Econ 703 Fall 2001 TA Ming Li What is NOT a proof 1 Providing examples in which the statement holds is not a proof Unless you can enumerate every possible case it does not suffice as a proof just providing examples However you only need one counterexample to disprove a statement For example you are asked to prove that the sum of an even number and an odd number is odd If you want to prove it by examples you would have to check it for all even and odd numbers which is an impossible task However if you want to disprove the statement that the sum of an even number and an odd number is even it suffices to give an example in which this does not hold N Showing that both the condition and the result are true is not a proof When proving a statement we should always start with supposing the condition given is true and use deduction to obtain the desired result In almost all cases the condition given is not always true in which case it is futile to try to prove the given condition E Saying the main point is obvious is not a proof There are main points you need to attack in a proof depending on the context in which the question is asked Reserve the word obvious for those statements that follow directly from trivial applications of definitions or straightforward algebra How to write good proofs l Precede your statement with we know from X that if it follows immediately from X where X could be a definition or a result that has been covered in the class or textbooks When you do your homework problems I do not encourage you to use results in the textbooks yet not covered in the class In many cases if you invoke an advanced result the statement to be proved becomes trivial 2 Use the format Claim before your statement when you are about to devote the following paragraph to proving this statement 3 Number your equations or intermediate statements when the proof is long Make explicit references to previously proven results for example it is preferable to write by equation 2 rather than as shown above I owe gratitude to the TA of one of the math courses I took as part of the material is taken from the handout he provided I also appreciate all the help and directions I have gotten from my past and present math teachers 4 V39 0 gt1 Avoid stating irrelevant facts These include but are not limited to restatement of basic de nitions unless it helps to clarify the goal of the proof implications of the given conditionthat play no role in obtaining the desired result excessive details etc Put your statements in logical order It is a good practice to use English words to connect parts of your proof and show your reasoning process Use good notation Follow standard notation Show all the arguments of a function whenever confusion is possible Learn the precise way of making a statement rather than using vague phrases like large enough close to zero almost equal etc Be careful with inequalities Distinguish weak inequalities from strict ones When you have a sequence of inequalities and equalities make sure each of them follows from definitions or known results Clarify if necessary You should not switch terms on both sides of an equality when that breaks off the logical order For example A B follows from definition 1 B 2 C follows from theorem 2 and your goal is to prove A 2 C Then you should not write B A 2 C A good way of writing it would be A B by definition 1 2 C by theorem 2 I
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