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PetePics Chapter 1 - Order terminology confusion

edited June 2018 in Discussion Groups

Index of picture posts

Revision history:
- 2018 06 18: Removed an unhelpful paragraph.
- 2018 05 26 : First version.

Comments

  • 1.
    edited June 2018

    picture

    Comment Source:![picture](https://i.imgur.com/qTEaVos.png)
  • 2.
    edited May 2018

    I find that the "light cone" visualization helps to fix some of the inconsistencies:

    This uses the Hasse diagram "smaller on bottom" order, but remains consistent with the standard symbols for "meet" and "join": the future light cone looks like a \(\vee\) for "least upper bound", and the past light cone looks like a \(\wedge\) for "greatest lower bound"). I still have to remember which symbol goes with which word, but things aren't quite so inconsistent from here.

    (In other words, I don't interpret \(\vee\) and \(wedge\) as arrows, but as cones of light emanating from a flashlight. Think about the negative space around the symbol, rather than the symbol itself!)

    I had a lousy time trying to memorize what made a "left adjoint" different from a "right adjoint".

    This comes down to the defining property, where if "f" is a left adjoint to "g", then "f" appears on the left of the \(\le\): \(f(x) \le y \Leftrightarrow x \le g(y)\).

    Comment Source:I find that the ["light cone"](https://en.wikipedia.org/wiki/Light_cone) visualization helps to fix some of the inconsistencies: <center>![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/470px-World_line.svg.png)</center> This uses the Hasse diagram "smaller on bottom" order, but remains consistent with the standard symbols for "meet" and "join": the future light cone looks like a \\(\vee\\) for "least upper bound", and the past light cone looks like a \\(\wedge\\) for "greatest lower bound"). I still have to remember which symbol goes with which word, but things aren't quite so inconsistent from here. (In other words, I don't interpret \\(\vee\\) and \\(wedge\\) as arrows, but as cones of light emanating from a flashlight. Think about the negative space around the symbol, rather than the symbol itself!) > I had a lousy time trying to memorize what made a "left adjoint" different from a "right adjoint". This comes down to the defining property, where if "f" is a left adjoint to "g", then "f" appears on the _left_ of the \\(\le\\): \\(f(x) \le y \Leftrightarrow x \le g(y)\\).
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