Definitions on the Trinity
The word "trinity" is a term used to denote the Christian doctrine that God exists as a unity of three distinct persons: Father, Son, and Holy Spirit. Each of the persons is distinct from the other, yet related in essence. Each is divine in nature, but each is not the totality of the Godhead.
The Father is not the same person as the Son who is not the same person as the Holy Spirit who is not the same person as the Father.
But in God there are not three entities, nor three beings. God, is a trinity of persons consisting of one substance and one essence. God is numerically one. Yet, within the single divine essence are three individual subsistences that we call persons.
Each of the three persons is completely divine in nature though each is not the totality of the Godhead.
Each of the three persons is not the other two persons.
Each of the three persons is related to the other two, but are distinct from them.
Athanasian Creed(fifth century)
http://www.carm.org/creeds/athanasian.htm We worship one God in trinity, and trinity in unity, neither confounding the persons nor dividing the substance.
And yet there are not three eternal Beings, but one eternal Being. So also there are not three uncreated Beings, nor three infinite Beings, but one uncreated and one infinite Being.
Thus the Father is God, the Son is God, and the Holy Spirit is God. And yet there are not three Gods, but one God only.
The Trinity is defined as one God who exists in three eternal, simultaneous, and distinct persons known as the Father, the Son, and the Holy Spirit.
A. Scriptural Evidence: (Quotations from The Works of B. B. Warfield, vol. 2, pages 133-135).
The term _"Trinity"_ is not a Biblical term, and we are not using Biblical language when we define what is expressed by it as the doctrine that there is one only and true God, but in the unity of the Godhead there are three coeternal and coequal Persons, the same in substance but distinct in subsistence.
By "trinity" I mean that within the nature of the one true God, there are three eternal, distinct Persons: the Father, the Son, and the Holy Spirit. These three persons are the one God. By using the logical technique called the transitive property of equality (things equal to the same thing are equal to each other), I will now demonstrate the biblical doctrine of the Trinity.
This essential teaching of Christianity states that we believe in one God who exists in three separate and distinct persons--God the Father, God the Son, and God the Holy Spirit. Each member is equal in nature and substance.
The Trinity Solves Problems
Gregory Koukl
The definition of the Trinity is this: there is one God, one Being who is God and only God; yet that one God has three different Persons, separate personas , the Father, Son and Holy Spirit. The Son is referred to as the Word in John 1. That's our view. Our view is not that the Father is the same as the Son. Our view is that the Father is not the Son. Our view is that the Spirit is neither the Father nor the Son. But that all are equally God. They possess everything that makes God God. They have God's nature and can be called God, yet there is only one God.