Dimensions in whole numbers are called integer.
Fractal numbers also play a role in dimensions and will be introduced later.
Dimensions in mathematical language:
point
D 0
0dimensional
line
D 1
1dimensional
plane
D 2
2dimensional
space
D 3
3dimensional
etc...
in general
D n
ndimensional
The mathematical view is an abstract view  there is no limit in numbers of dimensions.
 Dimensions are defined as degrees of freedom in movements.
dimensionality: degrees of freedom in movements
5 Dimensions
0  1  2  3  4 
Now we have descriptions of dimensions in 3 languages:
Language  Dimensions  
numerical  0  1  2  3  4 
mathematical  D 0  D 1  D 2  D 3  D 4 
geometrical  Point  Line  Plane  Space  no name 
Zero dimension and 4th dimension are added to the scheme.
Brief History of Ideas on Dimensionality.
To find out more about the 4th dimension, let's have a closer look to corresponding geometrical objects.
Lets Go Hyperspace
To be well prepared, use mathworld links in the last right column
dimension  geometrical  objects  mathworld links 
0  point 
 
1  line 
 
2  plane 
 
3  space 
 
4  hyperspace 

Projections:
PC screen is 2dimensional, a plane delivering a picture.
The picture of a cube on screen is the projection of a real (3D) cube on 2D.
For a cube many different projections are possible.
Mostly, our eyes recognize them immediately as a 3D cube object.
The other way round:
 The picture of a cube (2D) represents a real cube (3D)
To enter geometricalhyperspace (4th dimension), we use a simple geometrical construction law:
Abstract:
Visualized: "move perpendicular"
dimension  geometrical  perpendicular  move 
0  point 
 point 
1  line 
 line: 
2  plane 
 square: 
3  space 
 cube: 
4  hyperspace 

 Move Point A along the red line perpendicular to point B to get a line.
 Move red line (AB) perpendicular (along the green line) to position CD to get a square (ABCD)
 Move the square (ABCD) perpendicular (along the light blue line) to get a cube.
 .... don't move  just have a look at the animation of a tesseract building scheme.
Our imagination simply quits when we try to move a cube "perpenticular" to it's base, the space, in real.
But we can "construct" a 4D tesseract object by this law of moving perpendicular.
The above construction view of a tesseract is one of many possible projections of a tesseract.
[ projection of 4D onto 3D onto 2D ]
Next chapter shows a tesseract in motion (4D).