Bhagavad Gīta Bhāshya and Tātparya
B.G 2.20
na jāyate mriyate vā kadācin nāyaṃ bhūtvā bhavitā vā na bhūyaḥ । ajo nityaḥ śāśvato'yaṃ purāṇo na hanyate hanyamāne śarīre ॥2-20॥
He is never born, nor does it ever die; nor, having once existed, does it cease to be. The ancient living being is similar to the unborn Lord who is eternal, ever-existing, undying, and primeval; he is not slain when the body is slain.
Gīta Bhāshya 2.20
The word 'ajaḥ' here refers to the unborn Lord. The word 'purāna' refers to the living being as he travels from one 'pura', i.e. body, to the other. He is eternal in the same way always. The Supreme Ātmān whose essence is understanding, is unobstructed by place, time, state, or others. Living beings are eternal as they have some similarity with the characteristics of the unborn Lord.
atra mantravarṇo'pyastītyāha – 'na jāyata' iti॥ naceśvarajñānavad bhūtvā bhavitā। taddhi -'tadaikṣata' (chāṃ.u.6.2.3)।
Here, it is stated 'na jāyata' i.e. 'not born', as even vedic hymns reiterate the same. And like the knowledge of the divine, having existed it does not come into being. It is indeed stated, 'then he saw' (Chandogya Upanishad 6.2.3).
"deśataḥ kālato yo'sāvavasthātaḥ svato'nyataḥ। aviluptāvabodhātmā"
“The Supreme Ātmān whose essence is understanding is unobstructed by place, time, state, oneself, or others.”
(bhāga.3.7.5)
(bhāga.3.7.5)
ityādi śrutismṛtisiddham।
Thus, it is established as per the Vedas and Smritis.
kutaḥ? ajādilakṣaṇeśvarasarūpatvāt। śāśvataḥ sadaikarūpaḥ। puraṃ deham aṇatīti purāṇaḥ। tathā'pi na hanyate hanyamāne'pi dehe ॥20॥
Why (is living being eternal)? Because of its similarity with the characteristics of the unborn Lord. Eternally the Lord has a single, unchanging form. (The living being) is called 'purāna' as he travels from one 'pura', i.e. body, to the other. Thus, even when the body is being destroyed, it is not destroyed.
Gīta Tātparya 2.20
That which moves through ancient times, i.e. the living being, is called 'Purāṇa'. This living being is also unborn and eternal. Limited power, limited knowledge, dependence, incompleteness, and being a subsistence being are living beings' natural qualities. To be a living being, i.e. to be Jīva, is the opposite of being the 'Īswara', which means the Lord.
ayaṁ jīvo'pi ajaḥ nityaśca। anyathā punarukteḥ। śāśvataśca। na kadācidasvātantryādikaṁ jīvasvarūpaṁ jahāti।
This living being is also unborn and eternal. Otherwise, it would be a repetition. And he is perpetual as well. The living being never abandons its very nature of dependence and the like.
"alpaśaktirasārvajñyam pāratantryamapūrṇatā। upajīvakatvaṃ jīvatvamīśatvaṃ tadviparyayaḥ। svābhāvikaṃ tayoretat nānyathā syāt kathañcana। vadanti śāśvatāvetāvata eva mahājanāḥ॥"
“Limited power, limited knowledge, dependence, incompleteness, and being a subsistence being are living beings' natural qualities. To be a living being, i.e. to be Jīva, is the opposite of being the 'Īswara', which means the Lord. The great authorities declare that only these two are eternal.”
-iti mahāviṣṇupurāṇe।
- stated thus in Mahā Vishnu Purāna.
purāṇi aṇati gacchatīti purāṇaḥ ॥20॥
That which moves through ancient times, (i.e. the living being) is called 'Purāṇa'.

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बहुचित्रजगद्बहुधाकरणात् परशक्तिरनन्तगुणः परमः ।
सुखरूपममुष्य पदं परमं स्मरतस्तु भविष्यति तत्सततम् ॥
"The one who has created this variegated vast universe with varied forms has infinite power and is of infinite auspicious qualities. He certainly bestows the highest state of bliss to those who meditate on his ever happy essence." -Dwādasha stōtra 4.3

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