Is zero of nothing nothing? If so, would you write units for nothing?

I stumbled over a datasheet of an old pentode where it says, in the english translation:

I thought, wow, I am not sure if I wouldn't have written Ug3=0V instead. I am a theoretician in physics but work more as an engineer and teacher.

What happens inside of me seems to be the following:

1. The theoretical physicist screams, "are you crazy even to ask? 0 is zero. You don't want even units if there might be some. Better get rid of them somehow to have more general equations."
2. The engineer thinks about the following... What if asking someone external to measure a physical quantity and he wants to decide how to instruct the person. Would the engineer instruct to ask if
   
   1. the result is zero
   2. the person measured nothing regarding the measuring instructions
      
      and believes that the latter choice is better because it repeats intrinsically what has to be measured.
3. The teacher says: "If I begin a philosophical discussion now I am lost. I need to teach all the content and this question might be very confusing. It is better if the students always and ever write units instead of simply forgetting or ignoring them..."
   

This is just about your opinion and how you think. I am quite convinced that there is not a right or wrong.

Thank you for your thoughts.

This is the same discussion as of why the zero vector is a vector. It has neither direction nor length but a vector space without it wouldn't be a vector space.

I personally would prefer the notation ##0\,V## to avoid confusion and because of the vector space analogy. It is ultimately a measurement of voltage, regardless of whether it is zero or not. Technically, there is no difference between ##0## and ##0 \text{ times anything }.##

##0K, 0^oC, 0^oF## are all different temperatures.

Hill said:

##0K, 0^oC, 0^oF## are all different temperatures.

... but ##0\,mV##, ##0\,V## and ##0\,kV## are all the same voltage.

Hill said:

##0K, 0^oC, 0^oF## are all different temperatures.

Sure, okay, but this has nothing to do with voltage which is clearly relative to the grounding. 0V = 0kV = 0GV. I thought this is clear but you are right, I should have been more careful with the 0 and the units.

To get zero of something important enough to mention, you must subtract two things with the same dimensions. Whatever rounds down to zero, maintains its dimensions, so it can rise again, by the addition of more of the same.

Baluncore said:

To get zero of something important enough to mention, you must subtract two things with the same dimensions. Whatever rounds down to zero, maintains its dimensions, so it can rise again, by the addition of more of the same.

"Sorry, professor, I am not to very convinced by your arguments. I have questions...
I learned in math that I do just do things betweens numbers. I learned that there are mathematical objects like numbers or vectors. I learned the rules how to do mathematics between them. As an example, I can multiply a number with a vector. In the very beginning I learned that I can multiply numbers, like c = a*b. If a or b is equal to 0 the result is 0.

My physics teacher told me that numbers need suddenly units. Okay.
So, what you say is: There is an arbitrary number of zeros living in their own physical dimensions and waiting to be reborn or better born as the logical result as a process of substraction?

It makes only sense to have a resistance of zero Ohm because I could have negative Ohms?"

Well... all those childish questions.

Omega0 said:

My physics teacher told me that numbers need suddenly units. Okay.

Yes.
Before you add or subtract, the dimensional units of the numbers must be identical.
1 ohm + 1 ohm = 2 ohm.
1 ohm + 1 ohm - 2 ohm = 0 ohm.
1 apple + 2 oranges = bananas.

https://en.wikipedia.org/wiki/Dimensional_analysis

Omega0 said:

It makes only sense to have a resistance of zero Ohm because I could have negative Ohms?

Believe it or not, amplifiers have negative resistance.

Baluncore said:

1 apple + 2 oranges = bananas.

https://en.wikipedia.org/wiki/Dimensional_analysis

0 apples + 0 oranges = 0 fruit

I know a bit dimensional analysis but also I know a bit about the empty set in mathematics. As you might have seen in my post, in the top, this was not about a philosophical discussion if 1 apple +2 oranges may in the end be n bananas.
It was about the number 0 and if you feel that you need write a unit after the 0.

From your answers I would say that you "are the type"

5V -5V = 0V

and not the type

5V - 5V = 0

Did I get this right?

Is there a type ?

5.001 V - 4.999 V = 0.002 V = 2 mV .
5.000001 V - 4.999999 V = 0.000002 V = 2 μV .
5.000000 V - 5.000000 V = 0 V.
The result is still valid voltage data, even while it has a value of zero.

Omega0 said:

The theoretical physicist screams

I would not scream that. I always use units in this kind of situations. And also I put an arrow over zero when I write down zero vector.

The question is not if ##0V=0mV## but rather if ##0V=0K##. (The answer is, no.)

I'd say you should provide the unit, especially if it's a value that you've measured - 0mV implies quite a lot more precision than 0V unless you explicitly state ##\pm## values. But it's tolerable not to in many cases if the dimension being measured is obvious from context, particularly where it's a definition (e.g. "the value on this pin is the zero against which all voltage is measured', or "we define time zero to be when the collision occurred").

I've certainly written ##x=t=0## for something that I was defining as happening at the origin at time zero (even in non-geometric units where time and distance have different units). I would describe that as strictly wrong but perfectly comprehensible.

If you are measuring/counting things, you should identify the things. Physics is really, really, hard to do without keeping track of units, and it's impossible to communicate it to others. Be consistent, don't change styles/formats based on specific results.

BTW, yes there can be negative resistance. A gas discharge (plasma) is one example.

I too would prefer the field identified before the flagpole placed.

Zero is not an 'axle of all'.