The Isomorphism Theorems

We learned about quotient groups and four Isomorphism Theorems in my algebra class. My professor refers the four Isomorphism Theorems as “four siblings of Isomorphism Theorems” (of course, that made me laugh; it always makes me happy when people describe math in lively terms). I’ll write about my understanding of them in this post.

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An Idealized Programming Language

Imagine this: you write a program, compile it and you start to run the program. It has been running for one minute (“this is not a incredibly fast program”, you think;) five minutes (“oh, it’s kind of slow”), one hour (“okay it’s very slow”), one hour (you start to become impatient) and after one day, it’s still running. You start to wonder,

“would it ever stop running?”

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