Nill

A quantity is said to be nill, or negligible, if it is small enough that it can be ignored in the present context.

Nill is closely related to the standard mathematics concept of an infinitesimal, but it is not the same. Nill is also closely related to the concept of zero, but is not the same.

Examples

Examples

If a piece of paper is being considered in a context where one is measuring skyscrapers, its thickness is nill. The amount by which a piece of paper placed on top of a skyscraper augments its height is completely negligible.

If a scale measures weight in units of 0.1 pounds, then any object weighing much less than 0.1 pounds has nill weight.

Gas stations sometimes charge amounts of USD which are more precise than 1 cent, despite the fact that 1 cent is the lowest denomination of US currency. E.g. gas might be worth $3.782 per gallon. What this really means is that, when the customer has finished filling his car with gas, the amount charged to the customer is rounded to the nearest cent. For example, at the aforementioned price, if the customer purchases 13 gallons of gas, he will be charged $49.17, rather than $49.166 = 13 * $3.782. In this context, we say that any amount charged which is below $0.01 is nill.

Non-examples

In the context where a piece of paper is considered together with the hundreds of other pages of a book, the thickness of a piece of paper is not nill.

Contrast with infinitesimal

If a large number of nill quantities are added together, the resulting quantity will not necessarily be nill.

References

The name nill for this concept was coined by Harry Binswanger in his lecture Saving Math from Plato. [TODO rephrase or put this elsewhere in the document]