My course textbook writes this about weight spaces when talking about linear classification:
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Why would $w^{T}x$ be considered to be in the negative half space if 0 is not less than 0?
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Peter
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https://datascience.stackexchange.com/questions/68138/what-does-mathbfwtxw-0-graphically-mean-in-the-discriminant-function/81920#81920 – Graph4Me Consultant Oct 04 '20 at 21:15
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https://en.wikipedia.org/wiki/Half-space_(geometry)#Upper_and_lower_half-spaces – Graph4Me Consultant Oct 04 '20 at 21:17
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The text says "good region" and "bad region" and not "negative half space". The point is just that you have two half-spaces.. – Graph4Me Consultant Oct 04 '20 at 21:20