 Now what happens with subtraction? Well subtraction is just addition where one of these numbers is negative, but we haven't paid a lot of attention to the possibility of negative numbers thus far. So back up here with the linear multiplier, what if our multiplier wasn't 10, but it was minus 10? Would we expect our uncertainty to go negative? What does a negative uncertainty even mean? Ultimately we're talking about this delta x as just this distance, and so we're assuming that it's positive, and our value could be anywhere between x minus delta x or x plus delta x, or indeed possibly in the tails of some distribution of about that width. So we're really thinking about the uncertainty that we're quoting as a positive number, it's like the size of our uncertainty. And remember if this slope, if this graph went that way, we wouldn't expect to get a negative number therefore. So what we really should be doing is we should be putting an absolute value around whatever thing we get out of here, and that absolute value will make sure that our uncertainty comes out as a positive. And then it doesn't matter whether we pick plus or minus there, and it shouldn't. And it doesn't matter whether we pick plus or minus here, and it shouldn't. In the end what we're going to get is the sum of the uncertainties popping out. And so in fact addition or subtraction, in both cases, you add the uncertainties. So in other words supposing I go forwards a meter, plus or minus a centimeter, and then I go backwards a meter, plus or minus a centimeter. Now on average I end up at exactly the same place, but there's uncertainty. There's uncertainty on my step forwards, and then there's another different uncertainty on my step backwards, and so those uncertainties are not going to cancel. So I'm going to end up back where I started, but now I'm going to have an uncertainty of two centimeters from my starting position. So even though I'm subtracting the values, I'm subtracting my A and my B from each other, my measured values, I still have to add the uncertainties.