Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at firstname.lastname@example.org
The book cover is almost ready! Do you like it? What would you change?
This week, we’ve been working on a glossary of main terms. We wanted each definition…
Functions are machines that convert values to other values, or find correspondences between values. Function machines work by rules people make up. The starting values are called input. The converted or corresponding values are called output. The rule must find a single output for each input. Your stove is a function machine: it starts with the input of raw eggs, milk and spices, and makes the output of an omelet. The fantasy machine that starts with the same input and makes either omelets or live chickens is not a function.
What a function does, the inverse will undo. Of course, some deeds cannot be undone. The function of “baby drops a cup of grapes on the floor” has an inverse, “parental unit crawls around, searching for grapes and putting them back into the cup”. On the other hand, the function of “drop a cup of orange juice on the floor” and the function “break an egg for an omelet” do not have inverses.
Cycles are sequences of objects or series of operations that repeat. For example, “winter, spring, summer, autumn” is the cycle of seasons that repeats every year. There are cyclic stories and songs, like “99 bottles of beer.” Many household tasks are cyclic, such as washing dishes – “lather, rinse, repeat.” Cycles relate to recursion and iteration. Not all infinite sequences have cycles; for example, there are no cycles in the digits of Pi.
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Talk to you again on December 15th!
Moby Snoodles, aka Dr. Maria Droujkova