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Question Number 72900 by aliesam last updated on 04/Nov/19

prove that −∣a∣≤a≤∣a∣ a is a real number

provethat−∣a∣⩽a⩽∣a∣aisarealnumber

Answered by MJS last updated on 04/Nov/19

∀r∈R: ∣r∣:= { ((r; r≥0)),((−r; r<0)) :} ⇒ { ((a≥0: ±∣a∣=±a ⇒ −∣a∣≤a=∣a∣)),((a<0: ±∣a∣=∓a ⇒ −∣a∣=a<∣a∣)) :} ⇒ ∀a∈R: −∣a∣≤a≤∣a∣

∀r∈R:∣r∣:={r;r⩾0−r;r<0⇒{a⩾0:±∣a∣=±a⇒−∣a∣⩽a=∣a∣a<0:±∣a∣=∓a⇒−∣a∣=a<∣a∣⇒∀a∈R:−∣a∣⩽a⩽∣a∣

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