There are three main types of *ananta *(infinity).

1. *Parita-Ananta *(P. An.)

2. *Yukta-Ananta *(Y. An.)

3. *Ananta-Ananta *(An. An.)

Each of the above three types are sub-divided into three subtypes:

1. *Jaghanya *(Maximum)

2. *Madhyama *(Medium)

3. *Utkṛṣṭa *(Maximum)

Now let us consider these nine types of *ananta *as described in the Jain philosophy.

**1.**

*Jaghanya-Parita Ananta*(J. P. An.)By adding one in U. A. A., we get the value of J. P. An.. It means,

J. P. An. = (U. A. A.+1)

**2.**

*Madhyama Parīta Ananta*(M. P. An.)The numbers [(J. P. An.)+1] to [(U. P. An.)-1] are called M. P. An.. It means

[(J. P. An.)+1] ≤ M. P. An. ≤ [(U. P. An.)-1]

**3.**[(J. U. An.)-1] is known as U. P. An.

*Utkṛṣṭa Parīta Ananta*(U. P. An.)U. P. An. = [(J. U. An.)-1]

**4.**

*Jaghanya Yukta Ananta*(J. Y. An.)By raising J. P. An. to itself (*abhyāsa-guṇita*), we get the value of J. Y. An..^{[1]} It means

_{n}.)

^{(J. P. An.)}

**5.**

*Madhyama Yukta Ananta*(M. Y. An.)The numbers [(J. Y. An.)+1] to [(U. Y. An.)-1] are called M. Y. An., It means

[(J. Y. An.)+1] ≤ M. Y. An. ≤ [(U. Y. An.)-1]

**6.**

*Utkrsta Yukta Ananta*(U. Y. An.)[(J. An. An.)-1] is called U. Y. An.. It means

U. Y. An. = [(J. An. An.)-1]

**7.**

*Jaghanya Ananta Ananta*(J. An. An.)There are two definitions of J. An. An..

1. By raising J. Y. An. to itself (*abhyāsa-guṇita*), we get the value of J. An. An..^{[2]} It means-

_{n}.)

^{(J. Y. An.)}

2. By squaring J. Y. An., we get the value of J. An. An..^{[3]} It means

^{2}

**8.**

*Madhyama Ananta Ananta*(M. An. An.)Its definition is in two versions:

1. All the numbers from [(J. An. An.)+1] onwards are called (M. An. An.).^{[4]} It means

M. An. An. ≥ [(J. An. An.)+1]

2. The numbers from [(J. An. An.)+1] up to [(U. An. An.)-1] are called^{[5]} M. An. An.. It means-

[(J. An. An.)+1] ≤ M. An. An. ≤ [(U. An. An.)-1]

**9.**

*Utkṛṣṭa Ananta Ananta*(U. An. An.)According to Shvetamber (canonical) tradition, there is no existence of **U. An. An.**.

According to the Digambara tradition and the *Karmagrantha*, we get different definitions of **U. An. An.**. Again, in the Digambara tradition, we get three different definitions based on different definitions of V.-S. and difference in the sets of the infinite magnitude to be added. The fourth definition is of the *Karmagrantha *(which however is not believed to be canonical work in the Shvetambara tradition). We give here all the four definitions:

1. Firstly, J. An. An. is squared three times (i.e., it is raised to the power eight). Then the following six sets of infinite magnitude^{[6]} are added to the result obtained:

(1) The total number of *vanaspatikāyika jīvas *(vegetable bodied souls) of the whole universe.

(2) The total number of *nigoda jīvas*.

(3) The total number of *siddhas *(liberated souls).^{[7]}

(4) The total number of *paramāṇus *(ultimate atoms) of the whole universe.

(5) The total number of *samayas *of all time.

(6) The total number of *pradeśas *of the whole *alokākāśa *(supra-cosmic space).^{[8]}

Now, the magnitude thus obtained is again squared three times. Then to the magnitude obtained, the modes^{[9]} of the *kevalajāna *(omniscient knowledge) and the *kevaladarśana *(omniscient intuiion) are added. The magnitude thus obtained is called **U. An. An.**. There does not exist any object of this magnitude, and hence, it is of no use in empirical world.^{[10]}

2. The second definition of **U. An. An. **is as follows:^{[11]}

Firstly, **J. An. An. **is made to undergo operation V.-S. three times. Then the aforementioned six sets of *ananta *(infinite) magnitude are added to the magnitude obtained. Again, the obtained magnitude is made to undergo operation V.-S. three times. Now, to the magnitude thus obtained, the *avibhāgī pratīccheda *(indivisible units) of the *agurulaghuguṇa *(the quality of self sustenance) of the two *dravyas *(substances)- *dharmāstikāya *and *adharmāstikāya*- are added, and again the magnitude obtained is made to undergo the operation V.-S. three times. The final result thus obtained is denoted as '**U. An. An.**'^{[12]} This magnitude is equal to the (modes of) *kevalajāna *(omniscience). The mathematical computation which was made in the third definition of **U. A. A. **(see pp. 378-379) will be repeated here.

Thus, if J = **J. An. An.**

m_{1} = the sets added first time

m_{2} = the magnitude added second time

then,

III. The third definition of **U. An. An. **is given as follows^{[13]}:

The only difference in the II and III definitions is that instead of operation V.-S., here we use the operation '*śalakātrayaniṣṭhāpana*'.

**U. A. A.**

Thus, if

J_{1} = J. An. An.,

Then, by administering operation *śalakātrayaniṣṭhāpana*', we get the magnitude J_{4}.

Now, if m_{1} = the sets added, then

J_{4} + m_{1} = J′_{1}

Then, we can find the value of in J′′1 in the same way. Thus, we get

J_{4}` + + m_{1} = J_{1}" and so on up to J_{4}".

Then, **U. An. An. **= J_{4}"

IV. The fourth definition of **U. An. An. **is given as follows^{[14]}

The only difference in the III and IV definition is that here, after getting the value of J′_{4} -1, the *ananta *(infinite) *bahubhāgas *(indivisible units) of *kevalajāna *(omniscient knowledge) and *kevaladarśana *(omniscient intuition) are to be added to it. If it is denoted by m_{3}, then

**U. An. An.**= J′′

_{4}+ m

_{3}

This number is also in the form of *bhājana *(container) and not actual *dravya *(real substance). It means that there is no such object in the universe which has this magnitude.

Thus, even if there is difference in the different definitions of **U. An. An.**, but one thing is unanimously accepted that the value **U. An. An. **is only virtual, there being no substance actually existing, which has this magnitude.

Further research in the concept of *ananta *in Jain philosophy and that of infinity (α) in the modern mathematics is needed to evaluate the Jain philosophical view.

The total number of *abhavya jīvas *(souls) in the whole universe is also J. Y. An.. The souls which by nature are elligible for attaining the final emancipation (*moksa*) are called *bhavya *and those which are not so are called *abhavya*

*yuktānantaṃ tajjaghanyamabhyāsaparitāḍitam.*

*Nirekarūpamutkṛṣṭayuktānantakamāhitam..*

*atraikarūpaprakṣepe syādanantānantakaṃ laghu.*

* - Lokaprakāśa*, 1.179, 180

*jahaṇṇaeṇaṃ juttāṇaṃtaeṇaṃ abhavasiddhiyā guṇiyā aṇṇamaṇnabbhāso*

*paḍipuṇṇo jahaṇṇayaṃ aṇ aṃatāṇ aṃtayaṃ hoi.*

* -Aṇuogadārāiṃ*, *Sūtra *602.

*tadā jahaṇṇajuttāṇaṃtayaṃ sayaṃ vaggidaṃ ukkasajutāṇaṃtayaṃ adicchidūṇa jahaṇṇamaṇaṃtāṇaṃtayaṃ gaṃtūṇa paḍidaṇ. - Tiloyapaṇṇatti*, 4.312

*jaghanyayuktānante ca vargite rūpavarjite.*

*syādyuktānantamutkṛṣṭamityuktaṃ pūrvasūribhiḥ..*

*atraikarūpaprakṣepādanantānantakaṃ laghu. - Lokaprakāśa*, 1.200, 201

This opinion is of *Karmagrantha*.

*asmādyadadhikaṃ madhyānantānantaṃ ca tatsamm.*

*Utkṛṣṭa nantānantaṃ tu nāsti siddhāntināṃ mate.*

* Lokaprakāśa*, 1.180, 181

*teṇa paraṃ ajahaṇṇamanukkosayāiṃ, ṭhāṇāiṃ. se taṇ gaṇaṇāsaṇkhā.*

* Aṇuogadārāiṃ*, *Sūtra *603.

*Tiloyapaṇṇatti*, 4.313.

*prāgavedetadapi jeyaṃ madhyamutkṛṣṭa kāvadhiḥ- Lokaprakāśa*, 1.201

This opinion is of *Karmagrantha*.

The total number of *siddhas *(liberated souls) is *ananta *(intinite) but it is *ananta *(infinite) times less than the total number of souls. The total number of *nigoda jīvas *is *ananta *(infinite) times more than the total number of *siddhas *(liberated souls). The total number of *vanaspatikāyika jīvas *is *ananta *(infinite) times more than the total number of *siddhas *(liberated souls). The total number of *paramāṇus *of all *pudgalas *existing in the whole univer is *ananta *(infintie) times more than the total number of *jīvas *(souls) in the whole universe. The total number of *samayas *of all time (past, present and future) is *ananta *(infinite) times more than the total number of *paramāṇus *(ultimate atoms) *pudgalas *in the whole universe, and the total number of the *pradeśas *of the *alokākāśa *(supra-cosmic space) is *anantānanta *times (infinite times infinite times) more than the total number of *paramāṇus *of the *pudgalas *of the whole universe.

The knowledge and intuition of all the modes of all the substances (of *loka *and *aloka*) are respectively known as *kevalajāna *and *kevaladarśana*. The total number of their modes is *ananta *(which should be in the category of **M. An. An.**).

*Yajjaghanyayuktānantaṃ tadviralīkṛtyātraikaikarūpe jaghanyayuktānantaṃ datvā sakṛdvargitamutkṛṣṭa yuktānantamatītya jaghanyānantānantaṃ gatvā patitam.... yajjaghanyānantānantaṃ tadviralīkṛtya pūrvavattrīnvārān vargitasamvargitamutkṛṣṭanantānantaṃ na prānpoti, tataḥ siddhanigotajīva vanaspatikāyātītānāgatakālasamaya sarvapudgalasarvākāśapradeśadharmādharmāstikāyāgurulaghugu ṇānantān prakṣipya prakṣipya trīn vārān vargitasaṃvargite kṛte Utkṛṣṭānantānantaṃ na prāpnoti tato'nante kevalaj āne darśane ca prakṣipte utkṛṣṭānantānantaṃ bhavati.- Tattvārtha Rājavārtika, 3.38.*