this post was submitted on 29 Nov 2024
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Science Memes

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[–] OrganicMustard@lemmy.world 3 points 8 months ago (5 children)

You can make something like this properly by defining a different metric. For example with metric dl^2^ = dx^2^ - dy^2^ the vector (1, 1) has length 0, so you can make a "triangle" with sides of lengths 1, -1 and 0.

[–] kogasa@programming.dev 2 points 8 months ago (4 children)

That's not a metric. In any metric, distances are positive between distinct points and 0 between equal points

[–] technocrit@lemmy.dbzer0.com 0 points 8 months ago (1 children)

This is true for real-valued metrics but not complex-valued metrics.

https://en.wikipedia.org/wiki/Complex_measure

[–] kogasa@programming.dev 2 points 8 months ago

Metric, not measure. Metrics are real by definition.

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