A quick proof of the triangle inequality

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  1. Michael Penn
  2. math
  3. mathematics
  4. number theory
  5. abstract algebra
  6. calculus
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Комментарии
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Very well explained. These simple proofs can be made to appear terribly complicated. You have a great talent for explaining math.

kilianklaiber
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Now do the reverse triangle inequality,
| |x|-|y| | ≤ |x-y|

GhostyOcean
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Can someone give some examples when |x+y| < |x| + |y|?
I'm still failing to see the use of "<".

Tom-eghj
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But triangle inequality belongs to geometry?

كرمالكرد
Автор

This way of saying it makes it to complicated. If x and y are both positive then of course those will be equal. If they are each negative then numbers they will also be equal. And if 1 is negative while the other is positive then you will always get a smaller number than if you add them ignoring the negative sign, so it's true in all 3 cases. Don't need to introduce these "a" properties.

maxhagenauer
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