Hello again,There's no need to guess -- just do that math.
[in reference to: A>>1+R1/R2]
If it weren't dimensionless, then the units would be there. If it lacks dimensions, then it is dimensionless (seems rather obvious when put that way, doesn't it?).
This, of course, is only if the units are properly tracked in the first place. If someone is routinely sloppy with units, then it's not surprising that they would never have confidence whether a number in an equation is dimensionless or not because they are used to seeing dimensioned quantities presented as pure numbers and then just tacking on whatever units they think the answer should have regardless of the units that their work actually results in.
That's how we slam hundred million dollar space probes into planets or let airliners filled with passengers run out of fuel mid-flight.
Well we know that it 'should' be dimensionless for two reasons (and not because the units are not there):
1. 'A' is usually understood to be dimensionless.
2. R1/R2 is one resistance divided by another resistance or Ohms/Ohms which is dimensionless.
But in doing that we are taking the units from the context not from any stated or unstated units.
Now maybe it does not always work (track units as you said) but if we say:
R2>1
then since we have units of Ohms on the left we assume units of Ohms on the right. I've never seen anyone demand that we state the units for every single statement, although i agree that would be nice if they did. That would require writing:
"R2>1 with R2 in Ohms and '1' in Ohms."
Yeah sure if we had symbols it would be nice too:
"R2>1W"
where "W" here is used to represent "Ohms".
or even:
"R2>1R"
which is also typical.
Yeah your last line shows how problems can arise because of poor communication. That one time was a doozy too
I thought someone was just joking around when they told me for the first time that the thing crashed into Mars because of a units mixup. I still couldnt believe it i had to look it up to be sure. NASA=Not Always Sure About