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if a < b, then -b < -a

proof

if a < b then a-b<0 and b-a>0

so a-b<0<b-a

so -b<-a

Question

if a<b & c<0, then ab>bc

proof

if ac<ab then ab>bc

then ac<ab>bc

then ac>bc

Question

if a>1 then a^2>a

proof

a*a > 1*a

lemma 1: a*a = a^2

(a*a)*a^-1 = a^2 * a^-1

a*(a*a^-1) = a

a * 1 = a

a = a

so a*a>1*a

a^2>a

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# Help with a few questions about spivak calculus

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