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Question Number 152770 by naka3546 last updated on 01/Sep/21

$$Howtoprovethat$$ $$a<b<c\Rightarrow a+b>c$$ $$whicha,b,caresidesofatriangle?$$

Commented byMJS_new last updated on 01/Sep/21

$$a+b>c\wedge a+c>b\wedge b+c>a\iff a,b,c\mathrm{are}\mathrm{sides}$$ $$\mathrm{of}\mathrm{a}\mathrm{triangle},\mathrm{no}\mathrm{matter}\mathrm{if}a<b<c\mathrm{or}\mathrm{not}$$ $$\mathrm{we}\mathrm{cannot}\mathrm{prove}a<b<c\Rightarrow a+b>c\mathrm{without}$$ $$\mathrm{knowing}a,b,c\mathrm{form}\mathrm{a}\mathrm{triangle}$$ $$\mathrm{we}\mathrm{do}\mathrm{not}\mathrm{need}a<b<c\mathrm{to}\mathrm{prove}a+b>c\mathrm{when}$$ $$\mathrm{we}\mathrm{know}a,b,c\mathrm{form}\mathrm{a}\mathrm{triangle}$$

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