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When discussing question on another site, I came to a disagreement about rounding down negative numbers.

The two positions were:

  1. Rounding down is always toward negative infinity.
  2. It is ambiguous. It is defined as both rounding toward negative infinity as well as rounding toward 0.

The person with position 2, never quoted sources stating that rounding down is toward 0, and I suspect he is taking something out of context.

I have always been taught that rounding down is rounding to a smaller number (toward negative infinity), and rounding toward 0 is truncating.

Is rounding down always toward negative infinity?

ravery
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    In order to have any adequate discussion of mathematics, we need to have rigorously definitions of what processes, operations, and objects are being discussed. What do you mean by "round down." If you are referring to the floor function, yes you will find that for example $\lfloor -5.6\rfloor = -6$. The floor function of a real number (what many might call "rounding down") returns the greatest integer which is less than or equal to the input. In this case $-6$ is the largest number which is less than or equal to $-5.6$. – JMoravitz Oct 29 '18 at 01:56
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    There's not much point arguing about definitions. If you ever have to use the term, just make it clear what you mean by it. – Gerry Myerson Oct 29 '18 at 02:02
  • It is worth pointing out that some programming languages do prefer to talk about the integral part of a number as simply being everything to the left of the decimal point and the fractional part of a number as being everything to the right, in which case $\textbf{floor}(-5.6) = -5$. It is important to note that this is not a bad thing, the function used in python or C etc is simply not the same thing as the floor function commonly used in mathematics. They are both useful functions and they happen to agree on positive numbers but they should not be confused. – JMoravitz Oct 29 '18 at 02:03
  • @JMoravitz - Yes my understanding is that round down and floor are equivalent. ie rounding toward negative infinity. – ravery Oct 29 '18 at 02:51

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