Dear Srivatsan swami, adiyen’s humble namaskaram. After posting my reply to your query, I regreted; I should have waited for someone more knowledgeable to give you a detailed answer.
I say this because, I don’t know any detail about the ontology of Jivatma.
But there is one sentence in your query with a fallacy in it, and I wanted to address that. That is why I posted the verse. Now let me explain just this part; let us hope someone more knowledgeable will answer the deeper aspects of your question.
You said, “When some thing is a part of other, then both part and whole must be finite. Because infinity cannot be partitioned/divided”.
There is a fallacy in this statement, and this is addressed by the verse I posted. The verse is the invocation mantra for Sri Isopanishad. It means, “Perumal is the complete whole (Purnam); from Him emanates complete whole systems (with all the necessary things required to sustain themselves) (Purnaat purnam udachyathey); yet, even after so many complete systems emanate from Him (Purnasya purnam adhaya), Perumal remains the complete whole Himself, without any decrease. (Purnameva avasisyathey)”
In nutshell, “the Sum is greater than the parts”.
We can realise this fact through simple examples. First let us start with the example you have given. Infinity minus thousand is still infinity; infinity minus 100 thousands is infinity; infinity minus 100000 thousands is still infinity. How many ever thousands may ’emanate’ from infinity, infinity remains infinity! If all the thousands that ’emanate’ from the infinity are put together, still infinity remains greater than sum of all the thousands!
Another example: When you bring a small pin in contact with a magnet, the pin becomes a magnet. You bring 100 pins, all 100 pins can get magnetised, but that does not decrease the magnetism of the the original magnet in any way. When you put all the 100 pins together, still the magnetism of the original magnet is greater than the sum of all the pin magnets.
Another example: Our Swamy speaks; CDs are made of his speech; 1000s of CDs can be made from his speech; yet that does not decrease his original speech even an iota. You can put all the CDs ever produced together, yet his original speech and knowledge remains greater than the sum total of all the CDs!
Like this we can give many examples to help us see a glimpse of Perumal’s greatness. Sometimes some of the examples may have a defect; but Perumal’s greatness is inconceivable!
There are many things about Him we can not understand even through examples. For example, He can not be captured by even a great scheming person like Duryodhana; but He gets tied down to a mortar by a simple woman, His mother Yasoda. How can this contrast be explained?
The whole collection of universes are inside His belly; yet He can hide inside a simple mud pot! How can we explain this contradiction?
Everything that exists belongs to Him; yet He steals butter! How can this be explained?
There are so many things about Him like this! The first thing we need to understand about Perumal is that He is inconceivable. Once we accept this, then it becomes easier for us begin to see His greatness.
Kindly forgive me if, out of my ignorance, I have not understood your question and deviated way off from the original query.