Bhagavad Gīta Bhāshya
B.G 2.20
न जायते म्रियते वा कदाचिन् नायं भूत्वा भविता वा न भूयः । अजो नित्यः शाश्वतोऽयं पुराणो न हन्यते हन्यमाने शरीरे ॥ २-२०॥
The Lord is neither born nor does he die. The ever existent neither come into being nor ceases to exist. The Jīva transmigrating from one body to another is unborn, eternal, and permanent (as he is similar to Lord). The Jīva is not destroyed when his body is destroyed.
Gīta Bhāshya 2.20
Lord is eternal and the same always. Jīva is eternal, as he is similar to the Lord. But, he has a variance in knowledge, unlike the Lord. As Jīva travels from one body to another, he is called ‘purāna’.
अत्र मन्त्रवर्णोऽप्यस्तीत्याह– न जायत इति॥ नचेश्वरज्ञानवद् भूत्वा भविता। तद्धि -‘तदैक्षत’ (छां.उ.६.२.३)।
‘देशतः कालतो योऽसाववस्थातः स्वतोऽन्यतः। अविलुप्तावबोधात्मा’ (भाग.३.७.५)
इत्यादि श्रुतिस्मृतिसिद्धम्।
Even the Vedic hymns accept that the being is unborn. But unlike the knowledge of the Lord, knowledge of the being undergoes variations. It is so stated in ‘tadaikshata’ Vedic statement (chāṁ.u.6.2.3).
“In all places and time, in all states, without there being a difference in its nature or form, Lord with his knowledge is the same.” - bhāga.3.7.5
So he is famous in Vēdas and Purānas.
कुतः? अजादिलक्षणेश्वरसरूपत्वात्। शाश्वतः सदैकरूपः। पुरं देहम् अणतीति पुराणः। तथाऽपि न हन्यते हन्यमानेऽपि देहे ॥२० ॥
G.B 2.20.2
How is Jīva eternal? Because of its similarity with eternality and other qualities of the Lord. Eternally Lord has a single unchanging form. Jīva is called 'purāna' as he travels from one 'pura', body, to the other. Therefore, even when the body is destroyed, it does not cease to exist.

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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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