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A mini analysis of the infamous Archie’s comics. (Sexist???)

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FUN FOOD FOR THOUGHT

Books have been around for centuries. Novels, poetry, literature, fiction, self-help and almost anything else under the sun, as they are, after all, one of the quickest ways to spread knowledge and entertainment or simply a message to a large and varied number of people. A relatively newer addition to the seemingly never-ending list is the genre of comics. Filled with illustrations, more than the words, which are few, the pictures tell the story. Amongst this exciting new genre, is a rather well known type of comic book known as the ‘Archie’s comics’

The comics first debut, in December 1941, took the world by storm, fast becoming an international phenomena. These books proceeded to be sold in several different countries, thereby reaching a vast number of people.

While it is highly unlikely that the creators of these comics were misogynistic fiends, there is undoubtedly the presence of sexist implications…

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The classical inverse function theorem reads as follows:

Theorem 1 ($latex {C^1}&fg=000000$ inverse function theorem) Let $latex {\Omega \subset {\bf R}^n}&fg=000000$ be an open set, and let $latex {f: \Omega \rightarrow {\bf R}^n}&fg=000000$ be an continuously differentiable function, such that for every $latex {x_0 \in \Omega}&fg=000000$, the derivative map $latex {Df(x_0): {\bf R}^n \rightarrow {\bf R}^n}&fg=000000$ is invertible. Then $latex {f}&fg=000000$ is a local homeomorphism; thus, for every $latex {x_0 \in \Omega}&fg=000000$, there exists an open neighbourhood $latex {U}&fg=000000$ of $latex {x_0}&fg=000000$ and an open neighbourhood $latex {V}&fg=000000$ of $latex {f(x_0)}&fg=000000$ such that $latex {f}&fg=000000$ is a homeomorphism from $latex {U}&fg=000000$ to $latex {V}&fg=000000$.

It is also not difficult to show by inverting the Taylor expansion

$latex \displaystyle f(x) = f(x_0) + Df(x_0)(x-x_0) + o(\|x-x_0\|)&fg=000000$

that at each $latex {x_0}&fg=000000$, the local inverses $latex {f^{-1}: V \rightarrow U}&fg=000000$ are also differentiable at $latex {f(x_0)}&fg=000000$ with derivative

$latex \displaystyle Df^{-1}(f(x_0)) =…

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