Do you just mean that you shouldn’t use 0 as a probability (maybe only for an event in a countable probability space)? I agree with that, which is called Cromwell’s rule.
(Or, are you saying zero can never accurately describe anything? Like the number of apples in my hand, or the number of dollars you have in a Swiss bank account? Or, based on your own claim, the number of infinite sequences that exist? The probability that “the number of things that exist and match definition X is 0” is in fact 0, for any X?)
I would say 0 can be used to describe abstract concepts, but I do not think it can be observed in the real world. All measurements have a finite sensitivity, so measuring zero only means the variable of interest is smaller than the sensitivity of the measurement. For example, if a termometer of sensitivity 0.5 K, and range from 0 K to 300 K indicates 0 K, we can only say the temperature is lower than 0.5 K (we cannot say it is 0).
I agree 0 should not be used for real probabilities. Abstractly, we can use 0 to describe something impossible. For example, if X is a uniform distribution ranging from 0 to 1, the probability of X being between −2 and −1 is 0.
If I say I have 0 apples in my hands, I just mean 0 is the integer number which most accurately describes the vague concept of the number of apples in my hands. It is not indended to be exactly 0. For example, I may have forgotten to account for my 2 bites, which imply I only have 0.9 apples in my hands. Or I may only consider I have 0.5 apples in my hands because I am only holding the apple with one hand (i.e. 50 % of my 2 hands). Or maybe having refers to who bought the apples, and I only contributed to 50 % of the cost of the apple. In general, it looks like human language does not translate perfectly to exact numbers.
Do you just mean that you shouldn’t use 0 as a probability (maybe only for an event in a countable probability space)? I agree with that, which is called Cromwell’s rule.
(Or, are you saying zero can never accurately describe anything? Like the number of apples in my hand, or the number of dollars you have in a Swiss bank account? Or, based on your own claim, the number of infinite sequences that exist? The probability that “the number of things that exist and match definition X is 0” is in fact 0, for any X?)
I argue for infinite sequences in my other reply.
I would say 0 can be used to describe abstract concepts, but I do not think it can be observed in the real world. All measurements have a finite sensitivity, so measuring zero only means the variable of interest is smaller than the sensitivity of the measurement. For example, if a termometer of sensitivity 0.5 K, and range from 0 K to 300 K indicates 0 K, we can only say the temperature is lower than 0.5 K (we cannot say it is 0).
I agree 0 should not be used for real probabilities. Abstractly, we can use 0 to describe something impossible. For example, if X is a uniform distribution ranging from 0 to 1, the probability of X being between −2 and −1 is 0.
If I say I have 0 apples in my hands, I just mean 0 is the integer number which most accurately describes the vague concept of the number of apples in my hands. It is not indended to be exactly 0. For example, I may have forgotten to account for my 2 bites, which imply I only have 0.9 apples in my hands. Or I may only consider I have 0.5 apples in my hands because I am only holding the apple with one hand (i.e. 50 % of my 2 hands). Or maybe having refers to who bought the apples, and I only contributed to 50 % of the cost of the apple. In general, it looks like human language does not translate perfectly to exact numbers.