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0 pointskevinventullo7y ago0 comments

I'm not sure why that first plot wouldn't be considered continuous. There's a pretty clear positive correlation, which should be more pronounced with a non-log scale y-axis, and more pronounced as you increase the order of the curve.

I'm confused about the second plot; what order is the curve? It seems weird that there are no points between 10^12 and 10^156.

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ltbarcly36y ago

The second graph has a huge jump because the left side of the area I'm taking points from is a boundary between two very distant parts of the curve. In any space filling curve you will be able to find arbitrarily large jumps like this.

The difference would be more pronounced on a non-log scale, except the huge numbers at the top of the range would squish the graph down so you couldn't see what was going on.

The first graph isn't just not continuous, it's not even 1-1. (I'm ignoring the fact that is also discrete so that any formal sense of 'continuity' can't exist. Even if you tried to make it continuous by filling in the gaps it would be impossible.)

kevinventulloOP6y ago

Unfortunately I think we're talking past each other and this is not the best format for technical discussion.

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