Okay, as promised, here's a start to Epicurus's mention of "infinity, infinite" specifically using the term απειρον / απειρος. Below are only the mentions in the Letter to Herodotus with both Greek and English for comparison. One idiosyncrasy I noticed is that the translator likes to use "ad infinitum" where Epicurus uses εἰς ἄπειρον "to infinity". Granted, the Latin means the same as the Greek but it obscures Epicurus's use of the word he says we need to study:
Epicurus, Letter to Herodotus
37
Πρῶτον μὲν οὖν τὰ ὑποτεταγμένα τοῖς φθόγγοις, ὦ Ἡρόδοτε, δεῖ εἰληφέναι, ὅπως ἂν τὰ δοξαζόμενα ἢ ζητούμενα ἢ ἀπορούμενα ἔχωμεν εἰς ταῦτα ἀνάγοντες ἐπικρίνειν, καὶ μὴ ἄκριτα πάντα ἡμῖν <ἴῃ>42 εἰς ἄπειρον ἀποδεικνύουσιν ἢ κενοὺς φθόγγους ἔχωμεν.
"In the first place, Herodotus, you must understand what it is that words denote, in order that by reference to this we may be in a position to test opinions, inquiries, or problems, so that our proofs may not run on untested ad infinitum, nor the terms we use be empty of meaning.
41-43
"Ἀλλὰ μὴν καὶ τὸ πᾶν ἄπειρόν ἐστι. τὸ γὰρ πεπερασμένον ἄκρον ἔχει: τὸ δὲ ἄκρον παρ᾽ ἕτερόν τι θεωρεῖται: <τὸ δὲ πᾶν οὐ παρ᾽ ἕτερόν τι θεωρεῖται:>51 ὥστε οὐκ ἔχον ἄκρον πέρας οὐκ ἔχει: πέρας δὲ οὐκ ἔχον ἄπειρον ἂν εἴη καὶ οὐ πεπερασμένον.
"Καὶ μὴν καὶ τῷ πλήθει τῶν σωμάτων ἄπειρόν ἐστι τὸ πᾶν καὶ τῷ μεγέθει τοῦ κενοῦ. [42] εἴ τε γὰρ ἦν τὸ κενὸν ἄπειρον, τὰ δὲ σώματα ὡρισμένα, οὐθαμοῦ ἂν ἔμενε τὰ σώματα, ἀλλ᾽ ἐφέρετο κατὰ τὸ ἄπειρον κενὸν διεσπαρμένα, οὐκ ἔχοντα τὰ ὑπερείδοντα καὶ στέλλοντα κατὰ τὰς ἀνακοπάς: εἴ τε τὸ κενὸν ἦν ὡρισμένον, οὐκ ἂν εἶχε τὰ ἄπειρα σώματα ὅπου ἐνέστη.
"Πρός τε τούτοις τὰ ἄτομα τῶν σωμάτων καὶ μεστά, ἐξ ὧν καὶ αἱ συγκρίσεις γίνονται καὶ εἰς ἃ διαλύονται, ἀπερίληπτά ἐστι ταῖς διαφοραῖς τῶν σχημάτων: οὐ γὰρ δυνατὸν γενέσθαι τὰς τοσαύτας διαφορὰς ἐκ τῶν αὐτῶν σχημάτων περιειλημμένων. καὶ καθ᾽ ἑκάστην δὲ σχημάτισιν ἁπλῶς ἄπειροί εἰσιν αἱ ὅμοιαι, ταῖς δὲ διαφοραῖς οὐχ ἁπλῶς 53 [43] ἄπειροι ἀλλὰ μόνον ἀπερίληπτοι, [οὐδὲ γάρ φησιν ἐνδοτέρω εἰς ἄπειρον τὴν τομὴν τυγχάνειν. λέγει δέ, ἐπειδὴ αἱ ποιότητες μεταβάλλονται, εἰ μέλλει τις μὴ καὶ τοῖς μεγέθεσιν ἁπλῶς εἰς ἄπειρον αὐτὰς ἐκβάλλειν].
"Again, the sum of things (The All, τὸ πᾶν) is infinite (ἄπειρόν). For what is finite has an extremity, and the extremity of anything is discerned only by comparison with something else. (Now the sum of things is not discerned by comparison with anything else :64) hence, since it has no extremity, it has no limit ; and, since it has no limit, it must be unlimited or infinite (ἄπειρον).
"Moreover, the sum of things (The All, τὸ πᾶν) is unlimited (ἄπειρόν) both by reason of the multitude of the atoms and the extent of the void. [42] For if the void were infinite (ἄπειρον) and bodies finite, the bodies would not have stayed anywhere but would have been dispersed in their course through the infinite (ἄπειρον) void, not having any supports or counter- checks to send them back on their upward rebound. Again, if the void were finite, the infinity (ἄπειρα) of bodies would not have anywhere to be.
"Furthermore, the atoms, which have no void in them--out of which composite bodies arise and into which they are dissolved--vary indefinitely in their shapes ; for so many varieties of things as we see could never have arisen out of a recurrence of a definite number of the same shapes. The like atoms of each shape are absolutely infinite (ἄπειροί); but the variety of shapes, though indefinitely large, is not absolutely infinite. [43] [For neither does the divisibility go on "ad infinitum," he says below; but he adds, since the qualities change, unless one is prepared to keep enlarging their magnitudes also simply "ad infinitum." (ἄπειρον)]
45
"Ἀλλὰ μὴν καὶ κόσμοι ἄπειροί εἰσιν, οἵ θ᾽ ὅμοιοι τούτῳ καὶ ἀνόμοιοι. αἵ τε γὰρ ἄτομοι ἄπειροι οὖσαι, ὡς ἄρτι ἀπεδείχθη, φέρονται καὶ πορρωτάτω. οὐ γὰρ κατανήλωνται αἱ τοιαῦται ἄτομοι, ἐξ ὧν ἂν γένοιτο κόσμος ἢ ὑφ᾽ ὧν ἂν ποιηθείη, οὔτ᾽ εἰς ἕνα οὔτ᾽ εἰς πεπερασμένους, οὔθ᾽ ὅσοι τοιοῦτοι οὔθ᾽ ὅσοι διάφοροι τούτοις. ὥστε οὐδὲν τὸ ἐμποδοστατῆσόν ἐστι πρὸς τὴν ἀπειρίαν τῶν κόσμων.
"Moreover, there is an infinite number of worlds (κόσμοι ἄπειροί kosmoi apeiroi), some like this world, others unlike it. For the atoms being infinite (ἄτομοι ἄπειροι) in number, as has just been proved, are borne ever further in their course. For the atoms out of which a world might arise, or by which a world might be formed, have not all been expended on one world or a finite number of worlds, whether like or unlike this one. Hence there will be nothing to hinder an infinity of worlds (τὴν ἀπειρίαν τῶν κόσμων).
47
[47] "Οὐ μὴν οὐδ᾽ ἅμα κατὰ τοὺς διὰ λόγου θεωρητοὺς χρόνους αὐτὸ τὸ φερόμενον σῶμα ἐπὶ τοὺς πλείους τόπους ἀφικνεῖται -- ἀδιανόητον γάρ,-- καὶ τοῦτο συναφικνούμενον ἐν αἰσθητῷ χρόνῳ ὅθεν δήποθεν τοῦ ἀπείρου οὐκ ἐξ οὗ ἂν περιλάβωμεν τὴν φορὰν τόπου ἔσται ἀφιστάμενον: ἀντικοπῇ γὰρ ὅμοιον ἔσται, κἂν μέχρι τοσούτου τὸ τάχος τῆς φορᾶς μὴ ἀντικόπτον καταλίπωμεν. χρήσιμον δὴ καὶ τοῦτο κατασχεῖν τὸ στοιχεῖον. εἶθ᾽ ὅτι τὰ εἴδωλα ταῖς λεπτότησιν ἀνυπερβλήτοις κέχρηται, οὐθὲν ἀντιμαρτυρεῖ τῶν φαινομένων: ὅθεν καὶ τάχη ἀνυπέρβλητα ἔχει, πάντα πόρον σύμμετρον ἔχοντα πρὸς τῷ <τῷ>61 ἀπείρῳ αὐτῶν μηθὲν ἀντικόπτειν ἢ ὀλίγα ἀντικόπτειν, πολλαῖς δὲ καὶ ἀπείροις εὐθὺς ἀντικόπτειν τι.
[47] "Not that, if we consider the minute times perceptible by reason alone,69 the moving body itself arrives at more than one place simultaneously (for this too is inconceivable), although in time perceptible to sense it does arrive simultaneously, however different the point of departure from that conceived by us (...from the infinite). For if it changed its direction, that would be equivalent to its meeting with resistance, even if up to that point we allow nothing to impede the rate of its flight. This is an elementary fact which in itself is well worth bearing in mind. In the next place the exceeding thinness of the images is contradicted by none of the facts under our observation. Hence also their velocities are enormous, since they always find a void passage to fit them. Besides, their incessant (ἀπείρῳ) effluence meets with no resistance, or very little, although many atoms, not to say an unlimited number (ἀπείροις) , do at once encounter resistance.
56-57
"Πρὸς δὲ τούτοις οὐ δεῖ νομίζειν ἐν τῷ ὡρισμένῳ σώματι ἀπείρους ὄγκους εἶναι οὐδ᾽ ὁπηλίκους οὖν. ὥστε οὐ μόνον τὴν εἰς ἄπειρον τομὴν ἐπὶ τοὔλαττον ἀναιρετέον, ἵνα μὴ πάντα ἀσθενῆ ποιῶμεν κἀν ταῖς περιλήψεσι τῶν ἀθρόων εἰς τὸ μὴ ὂν ἀναγκαζώμεθα τὰ ὄντα θλίβοντες καταναλίσκειν, ἀλλὰ καὶ τὴν μετάβασιν μὴ νομιστέον γίνεσθαι ἐν τοῖς ὡρισμένοις εἰς ἄπειρον μηδ᾽ ἐπὶ τοὔλαττον.
[57] "Οὔτε γὰρ ὅπως, ἐπειδὰν ἅπαξ τις εἴπῃ ὅτι ἄπειροι ὄγκοι ἔν τινι ὑπάρχουσιν ἢ ὁπηλίκοι οὖν, ἔστι νοῆσαι ὅπως78 ἂν ἔτι τοῦτο πεπερασμένον εἴη τὸ μέγεθος. πηλίκοι γάρ τινες δῆλον ὡς οἱ ἄπειροί εἰσιν ὄγκοι: καὶ οὗτοι ὁπηλίκοι ἄν ποτε ὦσιν, ἄπειρον ἂν ἦν καὶ τὸ μέγεθος. ἄκρον τε ἔχοντος τοῦ πεπερασμένου διαληπτόν, εἰ μὴ καὶ καθ᾽ ἑαυτὸ θεωρητόν, οὐκ ἔστι μὴ οὐ καὶ τὸ ἑξῆς τούτου τοιοῦτον νοεῖν καὶ οὕτω κατὰ τὸ ἑξῆς εἰς τοὔμπροσθεν βαδίζοντα εἰς τὸ ἄπειρον ὑπάρχειν καὶ τὸ τοιοῦτον ἀφικνεῖσθαι τῇ ἐννοίᾳ.
"Besides, you must not suppose that there are parts unlimited (ἀπείρους) in number, be they ever so small, in any finite body. Hence not only must we reject as impossible subdivision ad infinitum (εἰς ἄπειρον) into smaller and smaller parts, lest we make all things too weak and, in our conceptions of the aggregates, be driven to pulverize the things that exist, i.e. the atoms, and annihilate87 them ; but in dealing with finite things we must also reject as impossible the progression ad infinitum (εἰς ἄπειρον) by less and less increments.
[57] "For when once we have said that an infinite (ἄπειροι) number of particles, however small, are contained in anything, it is not possible to conceive how it could any longer be limited or finite in size. For clearly our infinite (οἱ ἄπειροί) number of particles must have some size ; and then, of whatever size they were, the aggregate they made would be infinite (ἄπειρον). And, in the next place, since what is finite has an extremity which is distinguishable, even if it is not by itself observable, it is not possible to avoid thinking of another such extremity next to this. Nor can we help thinking that in this way, by proceeding forward from one to the next in order, it is possible by such a progression to arrive in thought at infinity (εἰς τὸ ἄπειρον).
60
[60] "Καὶ84 μὴν καὶ τοῦ ἀπείρου ὡς μὲν ἀνωτάτω καὶ κατώτατω οὐ δεῖ κατηγορεῖν τὸ ἄνω ἢ κάτω. ἴσμεν μέντοι τὸ ὑπὲρ κεφαλῆς, ὅθεν ἂν στῶμεν, εἰς ἄπειρον ἄγειν ὄν, μηδέποτε φανεῖσθαι τοῦτο ἡμῖν, ἢ τὸ ὑποκάτω τοῦ νοηθέντος εἰς ἄπειρον, ἅμα ἄνω τε εἶναι καὶ κάτω πρὸς τὸ αὐτό: τοῦτο γὰρ ἀδύνατον διανοηθῆναι. ὥστε ἔστι μίαν λαβεῖν φορὰν τὴν ἄνω νοουμένην εἰς ἄπειρον καὶ μίαν τὴν κάτω, ἂν καὶ μυριάκις πρὸς τοὺς πόδας τῶν ἐπάνω τὸ παρ᾽ ἡμῶν φερόμενον εἰς τοὺς ὑπὲρ κεφαλῆς ἡμῶν τόπους ἀφικνῆται ἢ ἐπὶ τὴν κεφαλὴν τῶν ὑποκάτω τὸ παρ᾽ ἡμῶν κάτω φερόμενον: ἡ γὰρ ὅλη φορὰ οὐθὲν ἧττον ἑκατέρα ἑκατέρᾳ ἀντικειμένη ἐπ᾽ ἄπειρον νοεῖται.
[60] "Further, we must not assert `up' or `down' of that which is unlimited (ἀπείρου), as if there were a zenith or nadir. As to the space overhead, however, if it be possible to draw a line to infinity (εἰς ἄπειρον) from the point where we stand, we know that never will this space --or, for that matter, the space below the supposed standpoint if produced to infinity (εἰς ἄπειρον) --appear to us to be at the same time `up' and `down' with reference to the same point ; for this is inconceivable. Hence it is possible to assume one direction of motion, which we conceive as extending upwards ad infinitum (εἰς ἄπειρον), and another downwards, even if it should happen ten thousand times that what moves from us to the spaces above our heads reaches the feet of those above us, or that which moves downwards from us the heads of those below us. None the less is it true that the whole of the motion in the respective cases is conceived as extending in opposite directions ad infinitum (εἰς ἄπειρον).
73
"Ἐπί τε τοῖς προειρημένοις τοὺς κόσμους δεῖ καὶ πᾶσαν σύγκρισιν πεπερασμένην τὸ ὁμοειδὲς τοῖς θεωρουμένοις πυκνῶς ἔχουσαν νομίζειν γεγονέναι ἀπὸ τοῦ ἀπείρου,
"After the foregoing we have next to consider that the worlds and every finite aggregate which bears a strong resemblance to things we commonly see have arisen out of the infinite (ἀπὸ τοῦ ἀπείρου).
74 in a scholia
[ἀλλὰ καὶ διαφόρους αὐτοὺς ἐν τῇ ιβ᾽ Περὶ φύσεως αὐτός φησιν: οὓς μὲν γὰρ σφαιροειδεῖς, καὶ ᾠοειδεῖς ἄλλους, καὶ ἀλλοιοσχήμονας ἑτέρους: οὐ μέντοι πᾶν σχῆμα ἔχειν. οὐδὲ ζῷα εἶναι ἀποκριθέντα ἀπὸ τοῦ ἀπείρου.]
[On the contrary, in the twelfth book "On Nature" he himself says that the shapes of the worlds differ, some being spherical, some oval, others again of shapes different from these. They do not, however, admit of every shape. Nor are they living beings which have been separated from the infinite (ἀπὸ τοῦ ἀπείρου).]
Our access to the papyri is paradoxically open and amazing but also at the same time limited and circumscribed by what was transcribed in the 19th century.
For me, an example of this idea would be that Epicurus was an ascetic as seems popular in some circles. A more plausible position from my perspective is that he may very well have tested himself from time to time to see how much he could live on and still be satisfied... but I certainly don't see him doing this day in day out. I have source amnesia but seem to remember one author talking about "from time to time" Epicurus would test the limits of this kind of thing and to better appreciate abundance when one has it. I think of Lent or Ramadan in a regular religious context.