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Show me a mathematical continuum in the real-world. And this is just the domain, nothing said about the mapping yet (the continuous function). Every analogy has
by mbeex 3y ago
Show me a mathematical continuum in the real-world. And this is just the domain, nothing said about the mapping yet (the continuous function). Every analogy has its limits.
- tomrod 3y agoThe space represented in a flat piece of paper. The space is continuous even if we can only measure down to the Planck length.
- mbeex 3y agoKey here: "represented" I'm only a mathematician, no physicist. But I think to remember, that the concept of a continuous physical space becomes quite muddled at this scale.
- nerdponx 3y ago"The space represented by the water in a convex container"
- hgsgm 3y agoIf you get to assume continuous paper, then I get assumed continuous paper. If you don't want to assume continuity, then you get it back by rephrasing your theorems as "within a margin of error equal to the distance between discrete objects".