Final answer:
A numerical value given to a dimension-less point on an image refers to a scalar indicating the degree of lightness or darkness of that point, relating to a value scale from white to black.
Step-by-step explanation:
A numerical value assigned to a dimension-less point on an image, such as the value indicating the degree of lightness or darkness on a grayscale, is essentially a scalar. A scalar is a physical quantity with magnitude but no direction, which contrasts with a vector having both magnitude and direction. An example of a scalar in geometry could be the coordinate of a point in a space which indicates its position relative to a frame of reference without implying any direction.
In the context of visual arts, the term 'value' refers to the relative lightness or darkness of a color, or more specifically, a shape within a design or composition. Hence, the value of a point in an image refers to its intensity on the value scale ranging from pure white to black. If we are looking at black and white digital images, for instance, each pixel value indicates the intensity of light, where 0 might represent pure black and 255 pure white (assuming an 8-bit grayscale).