#clock arithmetic

[math1089]

Clock Arithmetic: Understanding Modular Arithmetic with Timepieces

In the presence of so many beautiful creations of his thought the mathematician lives long and lives young: he rejoices in the grandeur of the height to which his controlled imagination attains.Robert D. Carmichael A clock is a device used to measure and indicate time. Normally, it displays the time in hours, minutes, and often seconds during a 12- or 24-hour period. In this blog post, we will…

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[isomorphismes]

These are my drawings of some simple groups: the "lightswitch group" ℤ₂, the "hi-lo-off lightbulb" ℤ₃, and the symmetric group 𝕊₃=ℤ₂×ℤ₃, which is how the letters {A,B,C} or the boyfriends {Pankaj, Nadir, Ajay} permute.

Edit: Several people have helpfully corrected me that 𝕊₃≠ℤ₂×ℤ₃. 𝕊₃ needs to be the twisted product of ℤ₂ & ℤ₃, not a straight product.

GLOSSARY

unary -- takes one argument -- like "square x"

binary -- takes two arguments -- like "x times y"

arity -- how many arguments a function takes

function -- the target needs to be unique (per source) but not the other way around

inverse -- when you can undo something

exponents -- superscripts representing how many times you apply a verb

[scigraph]

If/when we need to explain our system of time to the aliens…

the above graphic may come in handy. Taken from mathhen.