How is Brahman Anantam?

Question

Satyam Jnanam Anantam Brahman (Taittariya Upanishad 2.1.1)

Anantam means end less, which means you must be able to traverse it. As Brahman has no attributes an is devoid of differences how is it infinite? What does it mean?

For example, set of numbers is infinite, 1,2,3... to infinity. Now you will able to count 1, 2 etc indicating internal difference.

Another example is space, which is infinity, in space you can keep going and you'll never reach an end. So you can travel from here to there, that is why there is svagata bheda in space.

Same with time, time is infinite, but there yesterday, today and tomorrow.

Anything which is infinite seems to be by definition traversable, there should be some attribute which when traversed must not end. That is how a particular thing is infinite.

But how can this apply to Brahman, which is dimensionless, untraversable because it has no swagata bheda, and it has no attributes, which can be counted to make it infinite. It should be neither finite nor infinite. So how can a dimension less, Nirguna Brahman be infinite? What does infinity of Brahman even mean?

Answer 1

The very meaning of traversal of space/time may lose its relevance, without a point/frame of reference . However this subjective reference point is based on the perceiver.(A different anology in this empirical world could be , a dog may not see grass green owing to lack of rods and cones in its retina , but may grasp a sound in supersonic frequency(galtons whistle)) . So 'Grass is green', (similarly traversal,-- further, any extension of perception of objects by senses ,both made of panchabhootas) cannot be characterized as either as real or unreal , hence mithya.

Is traversal pivotal ,to prove infinity?

Here, the negative rememberance of I did not know anything then, proves the continuity of existence, following sushupti, hints the presence of Brahman which is the very awareness of the Jiva ,(not known by traversal).

sarvaprakārapramitipraśāntiḥ bījātmanāvasthitireva buddheḥ | suṣuptiretasya kila pratītiḥ kiṃcinna vedmīti jagatprasiddheḥ || 121 ||
Profound sleep is the cessation of all kinds of perception, in which the mind remains in a subtle seed-like form. The test of this is the universal verdict, "I did not know anything then".
Vivekachudamani(121) Wisdomlib

(concept of anthargatham and vyapakam)-

With Brahman as the substratum, Maya modifies itself into all the objects in the world, just like various pictures drawn on a wall. The first modification of Maya is space. Space derives its existence from Brahman. That is to say, space appears to exist only because of its substratum, Brahman, which is existence itself. It is Brahman or Existence which appears as akasa (space), but ordinary people and the logicians consider existence as a property of akasa. This wrong notion is due to Maya. Space has no existence apart from Brahman. Similarly, the other elements, air, fire, water and earth too have no existence apart from Brahman. They are not real in the absolute sense, but appear to be real because of the substratum, Brahman. Brahman is all-pervading, but the range of Maya is limited, that of space is more limited and that of air yet more so.
Summary of Panchadasi(Mahabhutaviveka) SN Sastri

When Maya is potential in Brahman( in the state of avyaktam), there is no space , thereby space isnt limitless,but is limited by Maya

Anantham is Svarupa lakshana-

As there is never a cessation/limitation for Brahman , Anantham is the very essence of Brahman (Thus Svarupa lakshana)

अवेद्योऽप्यपरोक्षोऽतः स्वप्रकाशो भवत्ययम् । सत्यं ज्ञानमनन्तं चेत्यस्तीह ब्रह्मलक्षणम्
Though beyond the reach of intellect, it is still immediately experienced for it is Self-luminous, Existence, Consciousness, Infinity are given (in Vedas ) as indications of Brahman.
Panchadasi ,Panchakosha viveka(28) M Srinivasa Rao and K A Krishnaswany Aiyer.Vani Vilas Press

Sadeva soumya Idam agra asit ekameva advidhiyam..chandhogya up(6.2.1)

(as a follow up of prev. ans.)

Answer 2

Brahman can't be described positively. However, Brahman can be described negatively. Below is an example of Brahman being described negatively.

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

Anantham is being applied negatively. What Brahman is not is being told. Brahman is not being described. So where is swagata bheda coming in the picture?

Why can't Brahman be described positively?

The answer is given in the Upanishads.

Brahman is beyond reason. For example, the Upanishads say poetically,

1. "The eye does not go thither, nor speech, nor the mind. We do not know It; we do not understand how anyone can teach It. It is different from the known; It is above the unknown. Thus we have heard from the preceptors of old who taught It to us."

(Kena Upanishad I.3-4)

2. "That which cannot be comprehended by the mind but by which the mind is cognized know that alone to be Brahman, and not this that people worship here."

(Kena Upanishad I.6)

3. "That from which all speech with the mind turns away, not having reached it, knowing the bliss of that Brahman, man fears nothing."

(Taittirya Upanishad II.9)

4. "He is never seen, but is the Seer; He is never heard, but is the Hearer; He is never thought of, but is the Thinker; He is never known, but is the knower. There is no other seer than He, there is no other hearer than He, there is no other thinker than He, there is no other knower than He. He is the Inner Controller - your own Self and immortal. All else but He is perishable."

(Brihadaranyaka Upanishad III.7.23)

Is it even possible in theory to describe Brahman positively?

The answer is no if you accept the Upanishadic teaching. In the usual case it is the human intellect that tries to understand a phenomenon. In the case of Brahman it is Brahman that runs the intellect. It is impossible for the human intellect to figure out how it's internal machinery is run.

Finally we can now answer how Brahman is anantham.

Om. That (Brahman) is infinite, this (universe) too is infinite. The infinite (universe) emanates from the infinite (Brahman). Assimilating the infinitude of the infinite (universe), the infinite (Brahman) alone is left.

Om Peace! Peace! Peace!

The Peace invocation of Brhadarayanaka Upanisad

The universe is infinite or endless because Brahman appears as the universe without any change in its nature. One can also turn it around. Looking at this infinite universe one realizes that Brahman is infinite since Brahman is appearing to us as the universe.