I think something there is some discrepancy in what I think of "approaching from above ( or below)" means and what @JohnBaez does.

Here is my picture of the situation for the right adjoint of the function \\(2\times -\\):

![adjoint2x](https://sites.google.com/site/testjustformevigg/_/rsrc/1528642702021/7sketches/20180609_094818.jpg?height=291&width=320)

The arrows for the floor function approach their target from above...

The same is true for the mini surjective function example by @Michael Hong:

![miniSurjective](https://sites.google.com/site/testjustformevigg/7sketches/20180609mini.jpg?attredirects=0)

Here, if \\(f\dashv r\\) (\\(r\\) is the right adjoint of \\(f\\), \\(f(1)= * \leq *\\) so \\(1\leq r( * )\\) then \\(r( * )=1\\) which I can only describe as "approaching from above".

In my Hasse diagrams, the order increases from to bottom, instead of from left to right. I am too used to doing it that way. Sorry for the hand-drawn pics, I don't have the skills or the patience to make them with the computer.

Here is my picture of the situation for the right adjoint of the function \\(2\times -\\):

![adjoint2x](https://sites.google.com/site/testjustformevigg/_/rsrc/1528642702021/7sketches/20180609_094818.jpg?height=291&width=320)

The arrows for the floor function approach their target from above...

The same is true for the mini surjective function example by @Michael Hong:

![miniSurjective](https://sites.google.com/site/testjustformevigg/7sketches/20180609mini.jpg?attredirects=0)

Here, if \\(f\dashv r\\) (\\(r\\) is the right adjoint of \\(f\\), \\(f(1)= * \leq *\\) so \\(1\leq r( * )\\) then \\(r( * )=1\\) which I can only describe as "approaching from above".

In my Hasse diagrams, the order increases from to bottom, instead of from left to right. I am too used to doing it that way. Sorry for the hand-drawn pics, I don't have the skills or the patience to make them with the computer.