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your mother said:

Where do you live, a.l.e.x59? It's unusual that you mention the lack of the number 4 in a building, because normally you only see that in Asian countries, specifically ones where Chinese is spoken.

Canada.

Anyhow, I've lived in several countries and this is what I can tell you:

[ Taiwan ]

Hospitals will never have 4, 10, 14 (or anything with a 4) or 13 marked as floors. The reason is because 4 & 10 sound very much like the word "death" in the Beijing Dialect, which is the official language of China and Taiwan. As for the number 13, well, it's just associated with bad luck. No hospital would like to have floors associated with bad luck or death!

No 0, 4, 10, 13, 14, 24, 34...? Do you know how many numbers those are? You might as well revert to alphabetically, differentiating the floors. I mean, if "10," and "4," sound like "death," in the Chinese dialect, than why not change their sounds? You cannot ignore the existence of such numbers, for they will always exist as is, and never be altered by merely changing the writing, which only serves as an understanding of the numerical law. Numbers have always existed, and their laws have always been so. Man only discovered them.

[ South America in general ]

Floors don't start with a 1. They start with PB, which means "Planta Baja" or "Ground Floor". Actually, this is the same in the UK and Hong Kong (being that they were a British colony). Some buildings have MZ for mezzanine but this depends on the building - whether it has a mezzanine or not.

Therefore, "Ground" is "floor 0." Why not write, "floor 0," if that is what it really is? It makes sense that the first floor in elevation is "floor 1," since the second centimeter line in a ruler is number 1, because there is 1 gap between the two lines, much like there is one gap between "floor 0," and "floor 1." Then again, we are not counting gaps, but the floors themselves. I don't know how to explain the answer, but "Ground" is not "floor 1," there may be a logical reason for this.

[ Hong Kong ]

Some buildings use 0 for the first, or ground, floor. 

Makes sense, oddly as it sounds. 0 must exist between 1, and -1, in order for all numbers to exist as a difference of 1 between each other.

The building where I work you have to punch in the floor number to call the elevator - there is no Up/Down button. Therefore, the ground floor is 1, and the basement is -1.

Here, "Ground" is 1. But in other buildings, "Ground" is 0. Which one does the numerical law follow? Only one can be true. If "Ground" is 1, and the floor beneath is -1, where is 0? If 0 does not exist between 1, and -1, there is a difference of 2 in between the numbers, which flaws the numerical law, since every number must have a difference of 1, from the next.

Can't think of any more cases at the moment...

It's all about superstition. Some people/cultures believe in it, but personally, I think that it's bad luck to be superstitious...

Superstition does not exist.