With all the above
clearly in our minds, we can say pointscumintervals in the measure
"before", or, "to the left of", zero should carry a little flag
(conventionally, '') indicating that, "we
are counting up,
but backwards/leftwards", or, "we
are lying to the left of zero".
We
could just as well put these flags on the intervals, "counting up, rightwards/forwards",
or, "lying to the right of zero".
It doesn't much matter where they go, provided we remember
that they are just there to keep us orientated, and provided that
we stick to our decisions about how to use them.
The
animation shows "+" flags on the numbers running right
from zero. These are very often simply omitted, as they are supposed
to be "tacit", or "understood", meaning, 'if
a plus sign is not there, the number is positive.'
This is
sometimes unhelpful, as zero and infinity are always unsigned. Moreover, occasionally we want to refer only to the value of a signed number (the socalled "absolute" value,
e.g., x). The confusion is compounded by statements like, "Absolute
values are always positive", which is simply untrue: they are
neither positive nor negative.
We also need
flags because, as we have seen, we are assigning the same numbers twice,
in two different senses.
The
issue of flagging and numbering is a source of enormous
and endless confusion, especially in classrooms,
in which it may for
instance be heard that, 'quantities can be less
than nothing', which is nonsense, or that, 'minus
times minus is plus', which seems like nonsense.
If we say,
"lying to the left or right of"
we
are speaking positionally.
We
are specifying where something is  passively. 
Passive
Flags 
On the other hand,
if we say,
"going rightwards/leftwards,
or,
forwards/backwards",
we are speaking operationally.
We
are doing something  actively. 
Active
Flags

So
our flags are also used twice, like the numbers: they
can be both passive signs and active operators.
So,
for example, when we multiply, we operate, and
when, operating, we multiply minus by minus, we are
simply issuing the command, "Reverse! Go the
other way round! Stop what you're doing, and do
the opposite!" We were "going left", or whatever the second minus meant, before,
so on multiplying by the first minus, we will be "going
right", or positively, after. Minus times a minus
is a plus. So simple, so easy to forget!
By this flagging scheme, neither zero nor infinity
carries a flagboth are unsigned.
Both mark a place where transition may be made
from the section with one sign to the section
with the other. Indeed, their roles may be swapped.
If we are to leave "plus territory" and enter
"minus territory", or vice
versa, we may do so only by way of one of these two places (this serves as
a reminder that one point does not divide a line;
two do).


Please do notice also that the numbers, as quantities, are always either zero, or more than zero, never less. They simply cannot be less.

