Video from crossexamined.org
"A tough question asked by a student at East Carolina University: If God is a limitless, infinite being how there can be a trinity?" from the introduction.
"...Readily visible below the cloud-line in the Bible is the truth that there are three divine persons who are one God. For example, “In the beginning was the Word, and the Word was with God, and the Word was God. . . . And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father” (John 1:1, 14). The Word “was” God and the Word was “with God.” Both God, and with God. Then, fourteen verses later, these two designations “Word” and “God” become “Son” and “Father.” And the Word/Son becomes “flesh” — truly human, the God-man. And “in him all the fullness of God was pleased to dwell” (Colossians 1:19).
And this God-man, the incarnate Son of God, spoke of the Holy Spirit as a distinct (third) person. “The Helper, the Holy Spirit, whom the Father will send in my name, he will teach you all things” (John 14:26). “If I do not go away, the Helper will not come to you. . . . When the Spirit of truth comes . . . he will glorify me, for he will take what is mine and declare it to you” (John 16:7, 13–14). Jesus is not speaking about a force, but a person — who teaches. And this person is distinct from the Son of God, for Jesus speaks of him as “another” person. And he is distinct from the Father, for “the Father will send” him.
Yet this person, the Holy Spirit, is also one with the Son of God. Jesus identifies the coming Helper like this: “You know him, for he dwells with you and will be in you” (John 14:17). Then in verse 25, he says, “I have spoken to you while I am still with you.” In other words, the Holy Spirit is one with the Son..." from the article: Can We Explain the Trinity?