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The key is distinguishing a time point from a minute displayed on a clock. My earlier sentence compressed that distinction too much.

Suppose we represent time continuously:

10:59:59.999 = before 11:00

11:00:00.000 = 11:00

11:00:00.001 = after 11:00

11:00:37 = 37 seconds after 11:00

11:00:59.999 = almost one minute after 11:00

11:01:00 = one minute after 11:00

So, mathematically, if the agreed start time is the instant T = 11:00:00, then:

on time if arrival≤T

and

late if arrival>T.

Thus an 11:00:37 arrival is:

11:00:37−11:00:00=37 seconds late.

Where the junior partner's argument comes from

There's a superficially plausible alternative interpretation. A digital clock displaying only hours and minutes will display “11:00” for an entire 60-second interval:

[11:00:00,11:01:00)

So at 11:00:37, it is perfectly correct to say “the clock says 11:00.”

But that doesn't establish that you arrived at 11:00. It establishes that you arrived during the minute labeled 11:00.

Those aren't the same proposition.

Consider:

“The train leaves at 11:00.”

If the doors close at 11:00:20, you wouldn't ordinarily say, “No problem, it's still 11:00.” The scheduled departure time denotes the beginning of that minute, not every instant for which a low-precision clock happens to display those four digits.

Same thing with:

“The filing deadline is 11:00.”

A document submitted at 11:00:45 is after the stated deadline unless some rule expressly defines the deadline with minute-level precision or provides a grace period.

There's also a revealing asymmetry

Take the junior partner's proposed rule seriously:

“As long as the clock says 11:00, you're on time for an 11:00 meeting.”

Then someone who joins at 11:00:59.999 is on time.

But someone joining one millisecond later at 11:01:00.000 is suddenly a full minute “late.”

That makes the permissible arrival window depend entirely on how many digits the particular clock displays, which is arbitrary. If his computer displayed seconds, his argument would presumably collapse at 11:00:01. If it displayed only hours, perhaps he could arrive at 11:47 because “the clock still says 11.” That's obviously not how scheduled times function.

But there are really two different questions

This is where I would qualify my original answer.

Was he literally late? Yes. If he joined after 11:00:00, he joined after the scheduled start time.

Was he late in the socially meaningful sense that normally warrants saying “you're late”? That's much less clear. Ordinary professional convention builds in some de minimis tolerance for synchronization, Teams latency, clicking the link, etc. Nobody sensible treats joining at 11:00:02 as equivalent to strolling in at 11:05.

So I think the senior partner wins the semantic/mathematical argument, pretty decisively. But that doesn't mean he wins the professional-conduct argument. A sensible formulation would be:

“Technically, you were 30 seconds late. Under ordinary circumstances, nobody would care. Given the CEO's explicit request for a prompt start, you should have been on a few minutes early.”

The junior partner picked a particularly bad hill to die on because “the clock still said 11:00” is not actually a good defense. The better response was simply: “You're right. The prior call ran over. Sorry.”

(https://autoadmit.com/thread.php?thread_id=5893096&forum_id=2#50067852)