Floor is not "the integer part of"?

I'm working through Assignment 3 again and I came across the floor function. This reminded me of something I started thinking about last year: Floor (x) is often defined informally as "the integer part of" and that's fine for positive numbers and zero, but is this definition true for negative numbers? As I understand it Floor (-2.5) = -3 whereas, the way I see it at least, "the integer part of" -2.5 is -2.

So, are Floor (x) and "the integer part of" not quite the same?

Tricky...

It would seem to make sense that, for positive numbers, the "integer part" is the same as the "floor", whereas for negative numbers the "integer part" is the same as the "ceiling".

However, not everyone uses this definition! If you use the "INT" function on a spreadsheet you will find that INT(-2.3)=-3, i.e. this is the floor. Care is needed.

In the footnote on Assignment 3 we were talking about positive numbers, but that's not clear in the footnote. I will change it to make this clear!

Floors, Ceilings, and INTs

Thanks.

I think computerphile (or was it Crash Course Computer Science?) had a video recently which mentioned a bug in a game which came about because one team of game developers had been using Floor() to work on the head of the main protagonist and the other had used Ceiling() to work on the body, and consequently the head didn't join the body :-)

I first noticed this point about Floor not quite meaning "the integer part of" when I used Desmos to plot Floor(x) and saw that it wasn't "rotationally symmetrical" (I'm not sure what the technical term is).

I should add that when I worked through these Assignments last year, I really enjoyed learning a little about the history of this function. Maths in schools is often completely "dehumanised", with no room for stories about the people involved, and how ideas developed over time: the short footnote about Floor and Ceiling helps bring the subject to life.

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