Notes on Mathematics: Form and Function by MacLane Acts Ideas Formulation Collecting Collection Set (of elements) Counting Next Successor Order Ordinal number Comparing Enumeration Bijection Cardinal number Computing Combination (of nos) Rules for addition Rules for multiplication Abelian group Rearranging Permutation Bijection Permutation group Timing Before and after Linear order Observing Symmetry Transformation group Building;shaping Figure;symmetry Collection of points Measuring Distance;extent Metric space Moving Change Rigid motion Transformation group Rate of change Estimating Approximation Continuity Limit Nearby Topological space Selecting Part Subset Boolean algebra Arguing Proof Logical connectives Choosing Chance Probability (favorable/total) Successive actions Followed by Composition Transformation group Table 1.1 from pg.35