We know that ‘point’ has theoretically no (i.e. zero) dimension, line has 1; plane has 2, and so on. Now, we also know that line is not simply a set of points, i.e. line can’t be thought of a collection of finite number of points. This is because 0*k=0, where 0 is the dimension of one point and k is the number of points.
Now, we can say that, if a point moves in space, its history in time produces a line. So, to make a line from a single point we need to traverse in the dimension of time, not only in space. So we can say that 0*T=L. Here 0 is the dimension of point, T is some quantity in time dimension and L is the length of the line produced by the movement of a point. This implies that [Constant in single dimension] /0 = [Some constant in time]. Important is, the basic idea behind this is quite general which is the value of something becomes infinity when we measure it in an inappropriate dimension. That’s why we get infinity in number system which should be definite in ‘time’/other dimension.
1 comment:
'Value of something' will never approach infinity because infinity is not a number.
Instead, 'value of something' will increase (or decrease as the case may be) without ending.
Try drawing a line segment EXACTLY 5 points long? Do you think it can be done? No matter what points you choose there will be infinitely many points between any two distinct points.
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