I was trying to explain Advaita, Dvaita and Visishta-advaita and not number theory. But I will explain number theory as well now.

From an infinite view-point all finites are its sub-sets and infinite makes them complete. That is advaita.

From any finite view-point, becoming infinite is not possible/practical. That is dvaita.

From a third party view-point, infinite seems to be a continuum of finite. That is visishta-advaita.

Infinity can be looked at in three different ways.

1. Poornam

2. Khahara

3. Ananta

Poornam is a bit like 'Advaitic' view. It is the view from the Infinity itself. 'Poornam' means complete. While infinity gives a sense of unlimitedness, poornam gives a sense of completeness.

What are the 'infinite' numbers between two real numbers say 3 and 4..? They are those real numbers that make it to 'complete' (poornam) from 3 to 4. What are the infinite numbers between two real numbers say 3 and 5..? They are those real numbers that make it to 'complete' (poornam) from 3 to 5.

And these two poornams/infinite numbers are equal poornams/infinite numbers. One is not bigger than the other. They are same. Mathematically this is proved by what is called 'Bijection theorem' (in one of the videos of PBS infinite series

here). This means even if we take out poornam/infinite from poornam/infinite, it still remains poornam/infinite.

That is the nature of Poornam, which is complete, makes complete and remains complete.

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[FONT=q_serif]पूणम् अदः पूर्णम् इदम् पूर्णात् पूर्णम् उदच्यते । पूर्णस्य पूर्णम् आदाय पूर्णम् एव अवशिष्यते".

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'khahara', which means 'divided by zero' and hence infinity is like dvaitic concept.

Here the view is from any limited real number. When any limited number is divided by zero becomes infinity. Similar to a dvaita concept, here the view of infinity is from limited number perspective. But dividing by zero does not make any practical sense and hence infinity is totally away from the grasp and realm of finite numbers.

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Then there is the concept of infinity which sees it as a continuation of finite numbers like the Visihta-advaita concept.

Ananta is the 'end-less'. This is the infinity concept of natural numbers, integers, odd numbers, even numbers etc where we indicate that endless as 'infinity' and see it as a continuation of finite numbers.

-TBT