Associativity is one of the first properties taught to students. Let's explore this property together.
For the curious among you, the mathematical theorem at the heart of this video is Cayley’s theorem for semigroups.
00:00 The equation
02:20 Exploration
13:36 What is associativity? Part 1
20:46 Application: group theory
25:20 What is associativity? Part 2
27:34 Reflections
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Function composition interpretation
Function as object: A machine taking input and transforming it into output
Function as action: modify any starting machine by connecting the output of another machine to its input
Object-object: A machine for which the output of a squaring machine is connected to the input of a square rooting machine is equivalent to an absolute value machine
Object-action: starting with a square rooting machine and then attaching a squaring machine to its input produces an absolute value machine
Action-action: attaching a square rooting machine to the input of any starting machine, then attaching a squaring machine to the input of the result is equivalent to attaching an absolute value machine to the input of the starting machine.
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