Luke 9:48 observes your care for others is the measure of your greatness.
When the disciples discuss being the greatest of all God does not reprove them for their desire but rather He refocuses them upon its proper accomplishment.
The One True God, the God of the Christian Bible, He alone defines greatness as service for others.
God modeled such greatness serving to the point of death as a substitutionary sacrifice for the evil all people from all time have committed against God. God lived as man among us not to be served but to serve and to lay down His life as a ransom for many.
God is great so it makes sense people made in His image would seek greatness. Our predisposition by birth is antagonism toward God and all His ways which causes us to redefine greatness by power, control and prestige. These are all the things God has and deserves, they are not for people.
While God holds all power, is able to control all things and demands all glory and honor exclusively He wields His power in humility with mercy and compassion showering all humanity with His kindness both toward the evil and the good.
The desire to be great reflects the greatness of God inherent to our origin. The definition of greatness as people understand it demonstrates our distance from God and inherent brokenness with God.
Those who would pursue greatness by God’s definition will become the servant of all, placing the needs and even desires of others above their own – a daunting task indeed.
No greater love has anyone than this, God said, that a person lay down his life for his friends. We are God’s friends, we demonstrate great love, when we lay down our will and ways to submit to God and His ways or as God said, we are His friends if we obey His commands.
The godly person will pursue greatness because God is great but they will define greatness God’s way which is the serving of others at personal cost no matter who they are or what it takes in order to help them be reconciled to God.