For uni I need to write a paper and give a presentation on intuitionism, and I am looking for nice examples of theorems or other results to prove or disprove intuitionistically. One example I found was that, intuitionistically, you can disprove the intermediate value theorem. As a counterpart to this I also want to prove another theorem or result via construction which you would otherwise or would typically prove by contradiction of its negation. Does anyone have nice examples of this I could use?
Any suggestions at all would be appreciated!!