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If-a-gt-b-and-c-gt-d-prove-that-a-c-may-be-greater-than-equal-to-or-less-than-b-d-

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Question Number 44502 by Tip Top last updated on 30/Sep/18
If a>b,and c>d,prove that a−c may be greater than, equal to or less than b−d.
Ifa>b,andc>d,provethata−cmaybegreaterthan,equaltoorlessthanb−d.
Answered by MrW3 last updated on 30/Sep/18
a=b+δ, δ>0 c=d+ϱ, ϱ>0 a−c=(b−d)+(δ−ϱ) (a−c)−(b−d)=(δ−ϱ) if δ>ϱ, (a−c)−(b−d)>0 ⇒a−c is greater than b−d if δ=ϱ, (a−c)−(b−d)=0 ⇒a−c is equal to b−d if δ<ϱ, (a−c)−(b−d)<0 ⇒a−c is less than b−d
a=b+δ,δ>0c=d+ϱ,ϱ>0a−c=(b−d)+(δ−ϱ)(a−c)−(b−d)=(δ−ϱ)ifδ>ϱ,(a−c)−(b−d)>0⇒a−cisgreaterthanb−difδ=ϱ,(a−c)−(b−d)=0⇒a−cisequaltob−difδ<ϱ,(a−c)−(b−d)<0⇒a−cislessthanb−d
Commented by Tip Top last updated on 30/Sep/18
Thank you Sir
ThankyouSir

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