Size of A Dot

[nycmathguy]

One of the very first things that I learned in geometry back in high school over 35 years ago is the fact that a dot has no measure, no size. Why is that the case?

 

[MathLover1]

In Geometry, we have several undefined terms: point, line and plane.

we define a point as a location and no size

 

[nycmathguy]

In Geometry, we have several undefined terms: point, line and plane.

we define a point as a location and no size

In other words, a point is not defined in geometry and thus we simply accept that there is no measurement.

 

[MathLover1]

we simply accept that there is no measurement because it's infinitely small to be measured

 

[nycmathguy]

we simply accept that there is no measurement because it's infinitely small to be measured

Ok. Cool.

 

[conway]

we simply accept that there is no measurement because it's infinitely small to be measured

If a "dot" or "point" on a number line is infinitesimally small. Therefore to small to be measured. Then this does not mean there is no dimension. It means only the dimension is to small to be measured.

Consider if a "point" or "dot" on a number line has NO dimension, then you can not move through it with mathematics. Movement requires dimension.

Further if a number line is by definition dimension. And a number line is composed of "points". Then how is it that the collection of dimensionless points gives rise to a dimension in the line. Much more logical to say that "points" are dimensions to small to be measured. Add a bunch of them together they become large enough to measure.

This also then proves that zero on a number line is dimension. Zero is a quantity of space. Thus one can solve for division by zero.

 

[conway]

In Geometry, we have several undefined terms: point, line and plane.

we define a point as a location and no size

It is impossible to have a "location", and "no size". Location by definition requires dimension. A point is a location with a size to small to measure. Yet the "size" is there.