Notes on Mathematics: Form and Function by MacLane

Acts               Ideas                Formulation
Collecting         Collection           Set (of elements)
Counting           Next                 Successor
                                        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
                   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