The Big Bang Theory is the prime theory to describe the beginning of the universe. George Gamov first suggested the concept in 1948. The theory explains how the universe emerged from a tremendously dense and hot point about 13.7 billion years ago. This point is called singularity. Precise prediction of background radiation temperature, even before its actual discovery, and recent findings, which suggest that our universe was much hotter in the younger ages, supports the Big Bang Theory. However, physicists have mainly avoided the conundrums of an infinitely compressed zero-sized starting point for Big Bang. The problem arises when we go to ultra small scales. We cannot find any meaningful size smaller than Planck length (10-^-33 cm) in objective universe. The Planck length is the building block of space. The only way that we can pass beyond this size is, if we exit the objective world and imagine singularity. Our objectivity based scientific laws do not govern in this arena. Any attempt to carry over these laws is doom to assumptions, uncertainty and confusion.

 

The question is how the zero point singularity can create the objective space-time universe.  Ordinal numbers can be suggested as a mathematical formalization for The Big Bang theory. Ordinal Numbers are the simplest set of all and is sometimes called empty set or null set.  The empty set is normally shown as,

 

Where the empty brackets delineate a set.  Since there is nothing inside the brackets it is an empty set. Let us associate Ø with the number 0. Then we can go further and define a set that its only member is Ø,

We use our logic to come to the deduction that { Ø } is not the same as  Ø. The set { Ø }  has one member on it, whereas Ø itself has none at all. Here we can associate {  Ø }  with number one. For number two we collect the two previous entities to come to,

 

 

Then we associate 3 with the collection of all the above sets as,

The number 4 is associated with the sets containing the members that we have encountered before to come to,

 

And so on. ⁵⁶

 

The concept of ordinal numbers shows how natural numbers can be derived from nothing. On the other hand natural numbers delineate different objective elements in space-time such as units of matter, space and time.  This concept can be used as formalism for the evolving objective universe from a zero-size, non-material singularity at the beginning of time.