We have always been given to believe that the state that you achieve when you realize Moksha and the experience of the highest truth is best described as Sat-chit-ananda. And this is often described as Truth-Wisdom-Bliss. Others describe it as that which is not asat(unreal), not achit (insentient) and not anananda (unhappiness). Yet others translate it as Eternal-Consciousness-Bliss or Absolute-Consciousness-Bliss. The second term - Sat-Chit-Anantha - appears to better describe the state, Sat-Chit being the ability to "see" or "perceive" the absolute truth, the attribute of a Seer, and Anantha is in this instance being the limitlessness of infinity. So "Limitless Wisdom", or in short the state of being "limitless". Which term and interpretation is right?
Let us first see what Advaita Vedanta means by Brahman.
The nature of Brahman that is the Self is, as we have seen, existence (sat), consciousness (cit),and bliss (ananda). Quoting from three different Upanisads, Sri Vidyaranyasays: "Uddalaka Aruni describes Brahman as existence (sat) by nature; in the Aiteraya Upanishad of the Rgveda, the nature of Brahman is indicated as consciousness (prajnana), and Sanatkumara refers to Brahman as of the nature of bliss (ananda)" (XIII, 63). Existence, consciousness, and bliss are not parts of Brahman, or its attributes; they constitute its essential nature (svarupa). They are not three separate constituents: existence is consciousness, and consciousness is bliss. It is because the world of plurality is characterised by impermanence, inertness and disvalue that in order to distinguish the non-dual Brahman from the world that Brahman is said to be existence, consciousness, and bliss. In Brahman's essential nature, however, there is no split and no distinction.
Introduction to Pancadasi of Sri Vidyaranya Swami translated by Swami Swahananda
What does it mean to say that the nature of Brahman is existence, consciousness and bliss? It does not mean that Brahman exists, is conscious and blissful. It means Brahman is existence itself, consciousness itself and bliss itself. Sat-Chit-Ananda captures this idea. What would Sat-Chit-Anantha convey? Can one say Brahman is Infinite itself? What would that even mean? Can one use the word Anantha as an attribute? No, since Brahman is not an object.
So Sat-Chit-Ananda is the correct way to describe Brahman in a positive way. It is unsafe to describe Brahman from the positive point of view because we have to be careful not to give Brahman any attribute or treat It as an object. It is safer to describe Brahman from the negative point of view, i.e., what It is not..
Brahman according to Yajnavalkya
Yajnavalkya said: O Gargi, it is the supreme being that the non-yogins call gross but, in fact, that is eternal and wonderful lord; one that is not long, not red, that has no head, that has no setting, hence that has a lasting taste, that has no contact, no smell, no juice, no eyes, no ears, neither speech nor mind, no brilliance, no proof [or magnitude], no (worldly) happiness, no name, no race, no death, no age, no ailment; that is nectarine, that is expressed by the word Om, that is immortal, that has neither a predecessor nor a successor, that is endless and non-external. It eats something. It does not eat anything. ..
Linga Purana II.9.53–54
However, you can use the word anantha as a stand alone word in the negative sense. In fact if you look at the second to the last line of the Linga Purana quote you will see that Brahman is being called endless.
Here, Lakshana (is definition), Lakshyartha(sought to be defined). according to nyaya.
In the context of Vedanta, where Supreme Brahman is the Lakshyartha , some of the categories of Lakshanas are
By distinguishing it from others (Vyavartaka Lakshana);
By pointing out its apparent attributes (Tatastha Lakshana);
By describing its essential nature (Svrupa Lakshana).
Eg. The Atman is distinct from Anatman (not-self) (Vyavartaka Lakshana).
Eg The Atman is the seeming substratum of the phenomenal universe (Tatastha Lakshana).
Eg Atman is essentially Satchidananda (Svarupa Lakshana).
Svarupa Lakshana as part of Vedas -
Satyam, Jnanam, Anantam, Brahma.
(Taittiriya Upanishad 2.1.1)
Prajnaanam Bramha (Aitareya Upanishad 3.3 of the Rig Veda)
VijnAnam Anandam Brahma (Brihadaaranyak upanishad 3.9 28.7) Here Jnana is chit
Though, Satchitananda seem to occur in prakarana texts, and several other scriptures as well , it isn't found in succession in Principal Upanishads. (afaik)
yatpratyastāśeṣamāyāviśeṣaṃ pratyagrūpaṃ pratyayāgamyamānam | satyajñānānantamānandarūpaṃ brahmādvaitaṃ yattadevāhamasmi
am verily that Brahman, the One without a second, which transcends the endless differentiations of Māyā, which is the inmost essence of all, is beyond the range of consciousness, and which is Truth, Knowledge, Infinity and Bliss Absolute.
Here , satya jñānān antam ānanda rūpaṃ also occur as Svarupa Lakshana, apart from Sat Chit Ananda.
Though Taittarēya Brahmānandavalli begins with ”Satyam-jñānam-anantam brahma” it does say “ānanda ātmā, brahma pucchaṁ pratiṣṭhā”. ,(also indicates atma is Ananda)
(Here Ananda (Bliss) beyond the Bliss in a mental state. it is the (default /essential) swarupa ananda)
Though some Swamijis (of an order) equate Anantha with Ananda by a substantial explanation, Swamijis (of another order) do not seem to say so. However (afaik) ,there isnt an explicit suggestion of it in scriptures .
Sense conveyed through various categories of Lakshanas, all of which are appropriate,do complement each other.