@Martin Sleziak I am a newcomer and may well be in the wrong room. A few days ago someone asked to show that if a/b and c/d were fractions and a,b,c, and d were positive, then (a+c)/(b+d) is less than or equal the max of a/b and c/d. I am not allowed to comment, but I wish someone would tell the poster about Farey addition and all the interesting things that follow from adding fractions the way we all wanted to in the beginning. Is it bad form for a banned commenter to say something here?