Question Number 152770 by naka3546 last updated on 01/Sep/21
$${How}\:\:{to}\:\:{prove}\:\:{that} \\ $$ $$\:\:{a}<{b}<{c}\:\:\Rightarrow\:\:{a}+{b}\:>\:{c} \\ $$ $${which}\:\:{a},{b},{c}\:\:{are}\:\:{sides}\:\:{of}\:\:{a}\:\:{triangle}\:? \\ $$
Commented byMJS_new last updated on 01/Sep/21
$${a}+{b}>{c}\wedge{a}+{c}>{b}\wedge{b}+{c}>{a}\:\Leftrightarrow\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{sides} \\ $$ $$\mathrm{of}\:\mathrm{a}\:\mathrm{triangle},\:\mathrm{no}\:\mathrm{matter}\:\mathrm{if}\:{a}<{b}<{c}\:\mathrm{or}\:\mathrm{not} \\ $$ $$\mathrm{we}\:\mathrm{cannot}\:\mathrm{prove}\:{a}<{b}<{c}\:\Rightarrow\:{a}+{b}>{c}\:\mathrm{without} \\ $$ $$\mathrm{knowing}\:{a},\:{b},\:{c}\:\mathrm{form}\:\mathrm{a}\:\mathrm{triangle} \\ $$ $$\mathrm{we}\:\mathrm{do}\:\mathrm{not}\:\mathrm{need}\:{a}<{b}<{c}\:\mathrm{to}\:\mathrm{prove}\:{a}+{b}>{c}\:\mathrm{when} \\ $$ $$\mathrm{we}\:\mathrm{know}\:{a},\:{b},\:{c}\:\mathrm{form}\:\mathrm{a}\:\mathrm{triangle} \\ $$