just a selkie in the sea

(I also go by Liz)

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footnote 33 is an incredible flex


Transcription:

Figure 4.11: If A and C are joined by a continuous chain of red and green countries, B and D cannot be joined by a continuous chain of blue and yellow countries.

is dealing with a map drawn on a plane) B and D obviously33 cannot be joined by a continuous blue-yellow chain (see figure 4.11). So one can change B's color to yellow by swapping blue and yellow in all blue-yellow countries joined to B. X can then be colored blue, so four-colorability is again preserved.

Footnote 33 text:

33. To Kempe, at least, it appears to have been obvious. To the modern mathematician, however, it is not a self-evident truth but a consequence of Jordan's curve theorem, which states that any simple closed curve on a plane divides the latter into two disjoint connected regions. The proof of this theorem is far from trivial, and the mathematical reputation of the intuitionist mathematician L. E. J. Brouwer (discussed in chapter 8) rested in part on his improved proof: Brouwer, "Beweis des Jordanschen Kurvensatzes," Mathematische Annalen 69 (1910): 169-175.

All text from Mechanizing Proof: Computing, Risk, and Trust, Donald MacKenzie


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