On this bite sized Irish video: https://www.youtube.com/watch?v=W261djbImqM

le saol na saol translates to world without end.

Google is telling me that le means with, saol means life and na means the.

Can somebody explain how translating la saol na saol to world without end makes sense? Seems like there could have been a more accurate translation. Thanks in advance!!!

In the religious context "world without end, Amen", is "saol na saol, Amen".

Saol = "world" or "age" nominative singular, but also "worlds" or "ages" genitive plural.
Na = the (plural)
saol na saol = literally "the age of the ages"
le = for.
Le saol na saol = for the age of the ages (=world without end, in the prayer).

[By the way, it is nitpicking, but her Irish is not perfect, and she pronounces the slender r like a broad r. She says "glór don athar", instead of "glóir don athair".]

Note: there is no reduplication of the article in Irish in genitive phrases. "The X of the X" is said in Irish as "X of the X". THE world of the worlds/age of the ages is "saol na saol". You can't put an article at the front of that. As "saol" is qualified by "na saol" (of the worlds/ages), it is already a definite phrase in Irish and doesn't need an article. Another example: Poblacht na hÉireann - the Republic of Ireland. As "Ireland" already makes the whole phrase definite, there is no article before "poblacht". Fear an tí - the householder, the man of the house. "An tí" is a definite qualifier and makes the whole phrase definite, so there is no separate article before "fear".

Declension of saol:

Singular
Nominative: saol
Genitive: saoil
Dative: saol

Plural
Nominative: saolta
Genitive: saol (but often saolta in the modern language outside of set phrases)
Dative: saolaibh (rarely used, so often saolta in the modern language too)

The short answer is that le saol na saol does not directly translate into "world without end".

It's worth pointing out that this prayer, the Gloria Patri, is very old, and dates back to at least the early 6th century. More importantly, the Irish version of the prayer provided by Bitesize Irish isn't a direct translation of the English version which they use. Both the English and Irish versions are probably derived originally from Latin, but the English translation is relatively loose compared to the Irish, which more closely resembles the original Latin and Greek forms of the prayer.

A closer translation for the Irish provided by Bitesize Irish would be the following:

Glóir don Athair, agus don Mhac, agus don Spiorad Naomh.
Mar a bhí ar dtús, mar atá fós, agus mar a bheidh go brách, le saol na saol.
Amen.

Glory to the Father and to the Son, and to the Holy Spirit.
As was in the beginning, as still is, and as will be forever, for the age of ages.
Amen.

For comparison, here are the earlier Latin and Greek versions:

Latin

Gloria Patri, et Filio, et Spiritui Sancto,
Sicut erat in principio, et nunc, et semper, et in sæcula sæculorum.
Amen.

Glory (to the) Father, and (to the) Son, and (to the) Holy Spirit,
As it was in (the) beginning, and now, and always, and in ages of ages.
Amen.

Greek

Δόξα Πατρὶ καὶ Υἱῷ καὶ Ἁγίῳ Πνεύματι,
καὶ νῦν καὶ ἀεὶ καὶ εἰς τοὺς αἰῶνας τῶν αἰώνων.
Ἀμήν.

Glory to the Father, and to the Son, and to the Holy Spirit,
Both now and always, and unto the ages of ages.
Amen.

Wow you guys are awesome! Thank you so much!

So.. Should I not trust google translate? It says that:

saol --> life
domhan --> world
aois --> age

Kind of a bummer of google translate is not a good tool... I have used it a decent amount so far

Domhan - world in the sense "God created the world"
Saol has translations ranging from life, to world to age. I think it might even derive from the Latin saecula, and it essentially means the world of men (we live in the world - the society and world around us).
Aois - age (middle-aged, what age are you?, etc).

As a rule, never trust Google translate outright, it's not uncommon for it to be wrong. To give it its due, it's not a bad tool. Most of the time it will render a translation which is, at least, interpretable. Someone who knows Irish will get the gist of what is being said, kind of like when someone who is learning English says things that sound a bit odd or makes grammatical errors, but you can still understand what they are trying to say. Still, it is only a tool, and it is not perfect. It will likely never be capable of giving translations which are as good as those a fluent human could.

It works by suggesting whatever it thinks is most likely to be the correct translation for whatever word, phrase or sentence you give it. Without any context, it will translate individual words like saol, domhan, and aois as "life", "world" and "age", as these are the most likely translations for these individual words in isolation. They are "correct" in the sense that those are acceptable translations for those Irish words, and probably the most common translations associated with them in whatever dataset Google uses to train it's models. Where there is more context available to the translation model than just a single word though, when you enter a whole phrase or sentence, the meaning of words can change based on that context. Think of the word "foot", for example. In most cases this word is likely to be a noun referring to that thing at the end of your leg. But, when it's used in the phrase "we foot it all the night", it's clearly a verb with a meaning like "run", "skip" or "frolic". You can only tell it means this, though, because of cues provided by other words in the sentence. So, don't be too hard on Google translate here. It's actually doing it's job as intended.

As for the phrase "world without end", it just so happens that this is very particular to this prayer. It's only ever really used in this context. The result is that Google has learned to translate the specific phrase idiomatically, in a way that to how it might translate the individual words which make up the phrase in isolation.