0<a<1
0<b<1
0<c<1
c=1-a-b
0<1-a-b<1
-1<-a-b<0
1>a+b>0
since 0<a, 0<b, there must be 0<a+b,
so we only need to test whether a+b<1 is satisified.
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0<a<1 0<b<1 0<c<1 c=1-a-b 0<1-a-b<1 -1<-a-b<0 1>a+b>0 since 0<a, 0<b, there must be 0<a+b, so we only need to test whether a+b<1 is satisified. 
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