Inequality Notation: What Does it Mean?

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Discussion Overview

The discussion revolves around the interpretation of inequality notation, specifically a notation involving dots that some participants suggest represents multiplication. Additionally, a question is raised regarding the applicability of the Pythagorean theorem in elliptical geometry, leading to a discussion on the relationship between the theorem and non-Euclidean geometries.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about a specific notation related to inequalities that they have not encountered before.
  • Another participant suggests that the dots in the notation represent multiplication, equating it to a standard inequality expression.
  • A separate question is posed regarding the validity of the Pythagorean theorem in elliptical geometry.
  • A participant responds that the Pythagorean theorem does not hold in elliptical geometry, stating it is equivalent to the parallel postulate, but mentions that generalizations exist for non-Euclidean geometries.

Areas of Agreement / Disagreement

There is no consensus on the interpretation of the inequality notation, as the initial inquiry remains open-ended. The discussion on the Pythagorean theorem also reflects differing views on its applicability in different geometrical contexts.

Contextual Notes

The discussion includes assumptions about the notation and the applicability of the Pythagorean theorem without fully resolving the implications of these assumptions in different geometrical frameworks.

j.gal
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I was reading on inequalities and encountered a notation i haven't come across before.
an image of it is added to this post as an attachment.
 

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If you mean the dots, it is simply a different way of expressing multiplication.

so that is the same as

(a)(c) > (b)(c)
 
one other question i have.
Does Pythagorean theorem still work if you use elliptical geometry?
 
No, the Pythagorean theorem is in fact equivalent to the parallel postulate. So it doesn't work in elliptical geometry.

There are however generalizations of Pythagoras which do hold in non-Euclidean geometry. More information can be found on wiki: http://en.wikipedia.org/wiki/Pythagorean_theorem
 

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