Concorde’s Cockpit.

Iceland

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

(via brittbutterfly21)

Half Of The United States Lives In These Counties

Lagrange's theorem

Theorem: The size of a subgroup of finite group is divisible by the group’s size. That is, if H is a subgroup of G, |H| is a divisor of |G|.

Proof: Let’s start by saying we have a group G and a subgroup H.

This proof will count cosets. Specifically, I’ll use left cosets, but right cosets work the same way. Also, this proof will rely on a few properties of the integers.

I’ll prove this through lemmas, which are theorems used to prove other theorems. The distinction between a lemma and a theorem is only based on how we use them, and so historical reasons might leave some theorems as “lemmas.”

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Title: Islandia

Map Maker: Abraham Ortelius

Place / Date: Antwerp / 1603

P-61 Black Widow cockpit.