
"And so too, (When Mashiach comes) the righteous will see and be glad, the upright will exult, and the devout will be mirthful with glad song." (Shmoneh Esreh, Yamim Noraim)

אֵין קִצְבָה לִשְׁנוֹתֶךָ, וְאֵין קֵץ לְאֺרֶךְ יָמֶיךָ, וְאֵין לְשַׁעֵר מַרְכְּבוֹת כְּבוֹדֶךָ, וְאֵין לְפָרֵשׁ עֵלּוּם שְׁמֶךָ. שִׁמְךָ נָאֶה לְךָ וְאַתָּה נָאֶה לִשְׁמֶךָ, וּשְׁמֵנוּ קָרָאתָ בִשְׁמֶךָ"There is no set span to Your years and there is no end to the length of Your days. It is impossible to estimate the angelic chariots of Your glory and to elucidate the hiddeness of Your Name. Your Name is worthy of You and You are worthy of Your Name, and You have included Your Name in our name." (Chazaras HaShatz Yamim Noraim)
This piyut is drawing a sharp contrast between feeble man and Almighty Hashem. The one preceding it, which ended describing the mortality of man, read: “We are but a dissipating cloud… flying dust, a fleeting dream…” The first words of this piyut, however, seem superfluous. First it says “There is no set span to your years (Hashem)…” and then it says “…and there is no end.” These two phrases mean almost the same thing but there is a slight difference. A ‘set span’ refers to an amount of time, so we are saying that Hashem has no life span, as it were, of like a billion or a trillion years. An ‘end’ refers to a deadline; so in effect, we are saying that Hashem’s existence is endless; He has no beginning and no end, which is coincidentally the 4th of the Rambam’s Ani Maamins.
The piyut ends with “And You included Your name in our name.”
Here are a few explanations of this:
-The Last 2 letters of יִשְׂרָאֵל are 'א' and 'ל' ; a Name of Hashem.
-When the Torah names the families of the Jews in Bamidbar, Perek 26, the letters of Hashem’s
name, 'י' and 'ה' are added to each name. For example: שָׁעוּל’s Family is called הַשָׁעוּלִי.
-If you spell out each letter of Hashems name ('י'and 'ה') You get yud, vuv, daled, and hei, and yud, and those letters spell out יְהוּדִי, Jew! (My favorite)
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(Clock pic courtesy of CoolChaser)
(Kippa pic courtesy of here)
אַחַת שָׁאַלְתִּי מֵאֵת ה', אוֹתָהּ אֲבַקֵּשׁ; שִׁבְתִּי בּבֵית ה' כָּל יְמֵי חַיַּי, לַחֲזוֹת בְּנֺעַם ה', וּלְבַקֵר בְּהֵיכָלוֹ
on and on. Finally you make your decision. You chose one of the many things you’ve taken into consideration, and give up the rest. That is how it works when dealing with a genie, but lehavdil eleph havdalos with Hakadosh Baruch Hu, the decision is easy. There are no cheshbonos, no calculations. If there is “One thing I ask of Hashem…This is the thing I want,” nothing else even comes to mind, the choice is clear. All I want is closeness with Hashem; a relationship with Avinu Shebashamayim.
Bris Avos (Covenant of the Forefathers). The Dover Shalom (Rabbi Shalom Rokeach, the first Belzer Rebbe) speaks about how this Eternal Love is referring to the times of Mashiach when Hashem's love for us will clearly be seen once we are no longer in exile under the subjugation of other nations. He also adds that with this Eternal Love and the covenant with our forefathers, Hashem will make the Mizbe'ach (altar) in the 3rd Beis Hamikdash eternal; there will never again be a churban (destruction). Another famous pshat, also told over in the name of the Dover Shalom, is that this bris mentioned here is the Bris Bein Habesarim that Hashem had with Avraham avinu, a covenant stating that Avraham's children will be many and basically that Hashem will ultimately redeem them, among other things. Finally- it is important to note that although the Zechus Avos (Merits of our Forefathers) may have run out according to Chazal, the Bris Avos is a Bris Olam, an eternal covenant.
around the world, they will be hated and persecuted! If I were trying to convince people that the Jews would last forever, I would say the total opposite! How will they ever survive if they are constantly persecuted and thrown out of their land? So it's pretty clear that no one in their right mind would make something like that up. So, like Abie Rotenberg said: "It had to be Hashem." (And btw- not only is it totally ridiculous for someone to make these contradictory predictions up, the crazy thing is-it's exactly what happened!!! Just look at Jewish History! A proof that Judaism is the true religion is simply the fact that we are still around. It's absolutely Yad Hashem (the Hand of G-d)! (Find out more about this typa stuff at Aish.com and Kiruv.com)
יָשִׂישׂ עָלַיִךְ אֱלֺקָיִךְ, כְּמְשׂוֹשׂ חָתָן עַל-כַּלָה
שׂוֹשׂ אָשִׂישׂ בַּה', תָּגֵל נַפְשִׁי בֵּאלֺקַי, כִּי הִלְבִּישַׁנִי בִּגְדֵי-יֶשַׁע מְעִיל צְדָקָה יְעָטָנִי, כֶּחָתָן יְכַהֵן פְּאֵר, וְכַכַּלָּה תַּעְדֶּה כֵלֶיהָ
כֺּה אָמַר ה': זָכַרְתִּי לָךְ חֶסֶד נְעוּרַיִךְ, אַהֲבַת כְּלוּלֺתָיִךְ, לֶכְתֵּךְ אַחֲרַי בַּמִּדְבָּר בְּאֶרֶץ לֺא זְרוּעָה
into an unsown land. We rushed so quickly that we didn't even wait for our bread to rise, and as a result, we have Matza. So that's why Hashem calls the holiday "Chag Hamatzos."