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On Mon, Apr 13, 2015 at 1:24 PM, Chris Barker <chris.barker@noaa.gov> wrote:

Because of these discontinuities, an equation wall(loc, t) = lt may have 0, 1
or 2 solutions.

This is where I'm confused -- I can see how going from "wall" time ("local" time, etc) to UTC has 0, 1, or 2 solutions:

One solution most of the time

Zero solutions when we "spring forward" -- i.e. there is no 2:30 am on March 8, 2015 in the US timezones that use DST

Two solutions when we "fall back", i.e. there are two 2:30 am Nov 1, 2015 in the US timezones that use DST

But I can't see where there are multiple solutions the other way around -- doesn't a given UTC time map to one and only one "wall time" in a given timezone?

Am I wrong, or is this a semantic question as to what "wall" time means?

You are right about what wall() means, but I should have been more explicit about knowns and unknowns in the wall(loc, t) = lt equation.

In that equation I considered loc (the geographical place) and lt (the time on the clock tower) to be known and t (the universal (UTC) time) to be unknown. A solution to the equation is the value of the unknown (t) given the values of the knowns (loc and lt).

The rest of your exposition is correct including "a given UTC time maps to one and only one 'wall time' in a given timezone." However, different UTC times may map to the same wall time and some expressible wall times are not results of a map of any UTC time.