Week 6: Proofs

The class continued how to write proofs with some different conditions such as proving inequality, existence, a sequence, non-boolean functions, using definition, proof by cases...We studied all these different cases but the structure of the proofs were basically same.

You start with the general assumption.

ex) Assume that n is generic natural number.

And then, use indentation on the next line in order to start an assumption under the initial assumption. You prove the process one in each line. At the end of each line, put '#' symbol and justify your process all the time. These assumption also need an indentation under the assumption. When you reached the last process, write the conclusion for the last assumption with the same position as the starting of the last assumption. Same thing with the other assumptions and conclusions.

ex)

Assume that n is generic natural number.

    Assume that...... #explain why

        Then, prove 1... #justify this proof

        Then, prove 2... #justify this proof

        .

        .

        .

        .

    Then, ...(conclusion), since assumed that... #assume that.....got (conclusion)

Then,......(complete conclusion), because n is generic natural number.

Above is the general format of proving example. This actually reminded me of  function recipe in python. When you write a body of function definition, if we use if, for, while, etc., we have to put an indentation on the next line which is the content of those. And when it's finished and return something, unindent the line back. I understood the format of proving, but if I don't know how to prove things, it wouldn't matter. So I guess the important thing is that I practice 'how to show that something is true\false'.