The following is a quote from a Trinitarian apologist website
While we must guard against separating the three personages (tritheism ) we must also be aware of the flaw of their being numerically one, they are Distinct but not separate. The church has always maintained the indivisibility of God, being so united that they are
three inseparable persons. The traditional doctrine called the perichoresis means the mutual indwelling of the three persons, in that each person permeates the other being united in substance. This guarded against any teaching that there are three separate Gods as in tritheism. That if God were deduced to a mathematical formulae he would not be 1+1+1=3 which would be tritheism, but would be 1x1x1=1, a unified one. None of the persons can exist without the other, they all make up the one God in unity. that each person dwells in the other two which makes God indivisible and unquantifiable, so that wherever one of the persons of God is, all of God is there. What we are not saying is that they separate nor physical.
http://www.letusreason.org/Trin7.htm
Any time a Trinitarian uses the word separate OR describes the persons as though they are separate like two persons in a room are separate, they have violated Trinitarianism and moved into the area of Tritheism
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