Great is the LORD, and greatly to be praised; and his greatness is unsearchable.
God is infinite! That’s the hardest thought I will ask you to grasp. You cannot understand what infinite means, but don’t let it bother you—I don’t understand it and I’m trying to explain it! “Infinite” means so much that nobody can grasp it, but reason nevertheless kneels and acknowledges that God is infinite. We mean by infinite that God knows no limits, no bounds and no end. What God is, He is without boundaries. All that God is, He is without bounds or limits.
We’ve got to eliminate all careless speech here. You and I talk about unlimited wealth, but there’s no such thing; you can count it. We talk about boundless energy—which I don’t feel I have at the moment—but there’s no such thing; you can measure a man’s energy. We say an artist takes infinite pains with his picture. But he doesn’t take infinite pains; he just does the best he can and then throws up his hands and says, “It isn’t right yet, but I’ll have to let it go.” That’s what we call infinite pains.
But that is a misuse of the words “boundless,” “unlimited” and “infinite.” These words describe God—they don’t describe anything but God. AOG004
Lord, Your greatness extends beyond the limitations of my human ability to comprehend. You are boundless, unlimited and infinite, and You are greatly to be praised. Amen. 
145:3 his greatness is unsearchable. That is, past the capacity of the human mind to fully describe or comprehend. It will take many worshipers, and a long duration (forever and ever, vv. 1, 2, 21), even to begin to do justice to what the Lord deserves.
145:3 his greatness is unsearchable Emphasizes that God—along with all of His worthy qualities—is simply too much for people to comprehend.
145:3 Great is the Lord. A standard affirmation in worship (35:27; 40:16; 48:1; 96:4) that alludes to the Lord as the great king.
unsearchable. God’s power and might are so great that finite human minds are unable to comprehend them fully. This verse teaches the doctrine of the incomprehensibility of God. People can have a true understanding of God but never a complete or exhaustive one.
 Tozer, A. W., & Eggert, R. (2015). Tozer on the almighty god: a 365-day devotional. Chicago, IL: Moody Publishers.
 Crossway Bibles. (2008). The ESV Study Bible (p. 1122). Wheaton, IL: Crossway Bibles.
 Barry, J. D., Mangum, D., Brown, D. R., Heiser, M. S., Custis, M., Ritzema, E., … Bomar, D. (2012, 2016). Faithlife Study Bible (Ps 145:3). Bellingham, WA: Lexham Press.
 Sproul, R. C. (Ed.). (2015). The Reformation Study Bible: English Standard Version (2015 Edition) (p. 1000). Orlando, FL: Reformation Trust.