Math CentralQuandaries & Queries


Question from Charlie, a student:

What is the smallest number? (i.e. the closest number to zero)

Hi Charlie,

It depends on what you mean by number. If you mean integer then 1 (or -1) is the closest integer to zero. I expect however that you mean rational number or real number. In this case there is no number closest to zero. You can see this by letting $x$ be any real or rational number that is not equal to zero. In this case the number $\frac{x}{2}$ is again a real or rational number and it is closer to zero then $x.$

There is however a mathematical object called an infinitesimal. According to Math World "An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity." It is not a number in the way we usually think about numbers. You can read more about infinitesimals in Wikipedia.


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