1. A dot is one-dimensional.

2. A surface is two-dimensional.
3. A cube is three-dimensional.

4. At is one-dimension.
5. At is the first dimension.

6. On is two-dimensions.
7. On is the second dimension.
8. On is two dimensions.

9. In is three-dimension.
10. In is three dimensions.
11. In is the third dimension.
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Which ones do we have to use?

The ones that make sense are #1, #2, #3, #9 should read... It is in three dimensions

#10 should read ... It is in three dimensions
#11 should read... It is in the third dimension. That is, the z-coordinate is in the third dimension.
Hope this helps : )

To understand which terms to use in the context of dimensions, we need to clarify a few points.

In points 1-3, you correctly define dot, surface, and cube in terms of their dimensions.

However, in points 4-11, it seems like you are trying to apply the concept of dimensions to words like "at," "on," and "in." It is important to note that these words have different meanings and cannot be directly equated to dimensions in the same way as objects or shapes.

The words "at," "on," and "in" are prepositions, which are used to indicate location or position. They do not inherently have a specific dimensional connotation, but rather describe relationships between objects.

For example:
- "At" is typically used to specify the position on a particular point or location, without indicating any specific dimensions. It does not relate to the concept of dimensions.
- "On" usually refers to the surface or topmost layer of an object or a location. While it could be associated with a two-dimensional aspect (since surfaces are two-dimensional), it is used to indicate location rather than dimension.
- "In" generally indicates something being enclosed within or contained by an object or a space, but it does not necessarily imply the concept of three dimensions. It is often used to indicate location or inclusion.

So, to summarize, you do not have to use "at," "on," or "in" as dimensions. Instead, they are prepositions that describe different aspects of location or position.