To break it down even further The Trinity entails the following:
1. Father, Son, Holy Spirit= One God, One Being/One Essence, co-equal, co-eternal. The single essence is shared corporately, collectively—within the three persons being co-equal and co-eternal, yet the essence or being of God is indivisible, simple not divided into parts. A kingdom divided will not stand [Matt 12:25, Mark 3:24-5]
2. Father, Son, Holy Spirit= all distinct persons, while having simultaneously three self-centers of consciousness but yet there are not three deities. The persons are not confused with the single essence. Just as we are all human in essence, yet we are not the same persons (see step 5).
3. Father, Son, Holy Spirit= each having different roles in what is called the economy of the Trinity. The Father chooses who will be saved (Eph 1:4). The Son redeems them (Eph 1:7). The Holy Spirit seals them (Eph 1:7) Jesus works in perfect unity with the Father and knows and performs the will of the Father (John 8:42), and yet also has a human will within one person of the Word incarnate in the hypostatic union (Truly God, Truly Man). This is why Jesus can claim he is The Truth (John 14:6).
"Just as God is unlimited or infinite with respect to time, so God is unlimited with respect to space. This characteristic of God's nature is called God's omnipresence (the Latin prefix omni-means 'all'). God's omnipresence may be defined as follows: God does not have size or spatial dimensions and is present at every point of space with his whole being, yet God acts differently in different places.
A good example of where Christians gain this thought from Scripture is Jeremiah 23:23-24 where God says "Do I not fill heaven and earth?" But throughout scripture there are other allusions to this thought (cf: Ps. 139:7-10; Col. 1:17; etc.).
5. There is a distinction between essence (being) and persons. Everyone is a (human) being, and also a person. The two terms are not the same. We are all human beings (sharing the same nature), yet different persons. We are all distinct from each other. There is a functional distinction; Being, and Person. Being is what we are. Person is who we are. Person within the Trinity is derived from the word Prosopon (Strong's Number: 4383, derived from the word Optanomai which means to look at, behold to allow one's self to be seen, to appear, visage), which means: the face, countenance (expression). Prosopon is the index of the inward thoughts and feelings the appearance one presents by his wealth or property, used in expressions which denote to regard the person in one's judgment and treatment of men, in essence, the outward appearance of inanimate things
6. The Word became Flesh (John 1:14): The Word took on flesh and has two separate natures, Divine and Human. There is no mixing, no dividing. Jesus is both truly God, truly man. When we understand the term “truly” as meaning completely, therefore it would follow that that there is no mixture of the divine with the humanity to make something completely new. Also there is no addition to either nature or depletion of either nature. In other words, to be fully complete is complete—not partial, this is the hypostatic union. The Word is God which emanates from the Father, and his Word is of himself, just as our words come from us, not of anyone else. This is a perfect union so it remains two complete and distinct natures of Christ within one person of Christ.