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A question on proofs

A question on proofs

av Sofia Tirabassi -
Antal svar: 1

Hello,

I got the following question from one of your colleague. Please refrarin to ask question like that by e-mail, ask them in the forum instead, so many can use my answer :)

I have a couple of questions regarding writing out proofs in the real analysis course. I come from a physics background so this is the first course that includes proper proofs for me. My 1st question is how do I know what’s assumed and what’s not when I’m gonna prove a statement? For example exercise 6 in the 1st chapter. How do I know whether (b^m)^n = b^(mn) is given/assumed true without a proof or should I prove it before using it? My 2nd question is: does the use of mathematical notation influence the grade one gets, meaning if I write there exists or I use the math notation for “there exists” would the grade be different? Im assuming you want us to hand in a latexed file for the homework. 

Som svar till Sofia Tirabassi

Re: A question on proofs

av Sofia Tirabassi -
Here is my answer:

Concerning question 1, you can assume basic arithmetic rules and all the statements we mentioned in the lectures so far as true (for the statement in the book please provide precise reference :)). If I required you to prove the rules of calculations for exponents, it will take hours to solve this exercise: you would have to construct the natural numbers, you will have to recursely define addition, multiplication. and show that they satisfy the usual rules of calculations by using induction. Then you define power and prove the rule, again using induction... too much work :) especially since the focus of this course is not logic, or foundations of mathematics, but analysis.

Concerning question 2:  No! The use of mathematical notation will not influence your grade. Writing style differs a lot from subject to subject, but I come from a school in which quantifiers are good on notes and blackboards, but not when one typewrites. Thus I would much prefer one to use words instead of symbols when writing. The same is true for arrows. I prefer "If... Then" to $\Rightarrow$ and "if, and only if,..." to $\Leftrightarrow$. In the slides you migt see me using "iff", instead of "if, and only if...". This is because I was a bit lazy in typing them. You will never see me write iff in an article, grant application or similar :)
And if you ever ask me a thesis, or I am the gränskare of your thesis, I will complain a lot about the use of symbols arrows and iff in the text :) (so that you are prepared)

I hope this helps
Sofia