11. Multiple Divisions

Multiple Divisions

Division gives us the ability to see that topology plays a very important role in showing that the one way function exists. It allows us to see the permutations of a monomial decider.

Exercises

1. How would your representation look like if you had multiple divisions?

2. Can you find the permutations of all the divisions? By doing so, you have shown that it is a topology which will be the next step.

3. Your representation of m(x) and all the division operation forms the base of a topology. Show that it is a topology by definition.

1. Both the empty set and your representation of the operations of division, X, are elements in your space.
2. Permutations intersect and the union of two elements is an element in the space of m(x).
3. Any intersection of finite elements in your space is an element in your space.

4. When you take the union of two elements in your space, is the representation of the division operations the same?