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mark 2025-01-21 21:46:18 -08:00
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5
src/Advanced/Tropical Polynomials/parts/00 arithmetic.typ
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@ -61,7 +61,10 @@ Let's expand $#sym.RR$ to include a tropical additive identity.
#problem() #problem()
Do tropical additive inverses exist? \ Do tropical additive inverses exist? \
#note([Is there an inverse $y$ for every $x$ so that $x #tp y = #sym.infinity$?]) #note([
Is there an inverse $y$ for every $x$ so that $x #tp y = #sym.infinity$? \
Remember that $#sym.infinity$ is the additive identity.
])
#solution([ #solution([
No. Unless $x = #sym.infinity$, there is no x where $min(x, y) = #sym.infinity$ No. Unless $x = #sym.infinity$, there is no x where $min(x, y) = #sym.infinity$