Direct Proportions

Hello mathematicians, puzzlers, and other curious people!

I mentioned a rabbit trail in a previous MMusing, when I used the word \”group\” about functions in the form f(x)=kx, called direct proportions. I didn\’t run down that rabbit trail that day. Let\’s do it today.

In ordinary English, a group is any collection of things — similar to what we call a set in mathematics. However, when we\’re speaking mathematically, there are some strict rules that a set has to follow to be called a group, called the Group Axioms.

First we need to choose a set we want to investigate. For this example we\’re going to use the set of all direct proportion functions, like f(x)=5x and f(x)=0.3x and f(x)=-1x. (You can also investigate groups like the symmetries of regular polygons or polyhedra. There goes another rabbit!)

Click here to read the whole Mathematical Musing