Saturday, August 28, 2010

Interesting point about set theory

Picture a set of measure zero, and picture a set with empty interior.

IMO: To me, these two differ in terms of mental image, FWIW. Shows how "mental images" can differ for different individuals at the very least. Indeed one could probably make a lot of philosophical and psychological points about consciousness etc on the matter. Reading the n-category cafe, “measure zero” is different from “empty interior”—even for compact sets—precisely because Lebesgue measurability is different from Jordan measurability

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