|a| = 0 iff a = 0 (Proof) [ILIEKMATHPHYSICS]

This video references "Intro to Real Analysis" by Bartle and Sherbert Fourth Edition. For more details related to the context of this video, see section 2.2.
This fact is not proven in the book. However, it stated in the book after Definition 2.2.1 that this fact follows from the definition, which is what we demonstrate here. But also note that we use another fact which comes from Definition 2.2.1, namely if A ≠ 0 then |A| ﹥0. This fact essentially is the contrapositive of the forward.
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