Can You Prove the Triangle Inequality?

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We prove the triangle inequality, |x+y| is less than or equal to |x| + |y|. This is a proof that is often shown in discrete math or real analysis.

#TriangleInequality #MathProof #discretemathematics

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Комментарии
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Only cool kids can prove triangle inequalties.

I know there are other proofs. Share them if you know them.

Trevtutor
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you saved me on my quizes like 5 times for now, you are really are a savior.

AhmedAbdelbaset-zb
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All my homies can prove triangle inequalities, mad respect man

sagejpc
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I never could understand how we jump from -(|x|+|y|) to |x + y|. Aren't we supposed to shoe that somehow? In the video you said we make the "logical conclusion" that this is true. Take x = -1 and y = 2. Does the first expression yield not 1 + 2 = 3, and the latter -1 + 2 = 1?


Oh or perhaps we are coming from a point of like sort of "having proved" that the quote-unquote logical conclusion is true? Like i have just proven the RHS above with my chosen values, and the <><><> like we're not necessarily saying that the two (LHS) expressions are equal, just that the two EQUATIONS (both LHS & (similar) RHS) are true? Just that, that they are both true? Oh, i think this is it yeah. I do still feel like these (unsimilar) LHS should be somehow equated tho no? Or equatable at least?

chuhu