Christianity has its roots in Judaism, as such some of the teachings in the Old Testament have carried into and are reaffirmed in the New Testament, one such being is the monotheistic belief in one God. When Jesus is asked which is the most important commandment he replies:
Mark 12:29 "The most important one," answered Jesus, "is this: 'Hear, O Israel: The Lord our God, the Lord is one..
This is reminiscent of Deuteronomy 6:4 in the Old Testament:
Hear, O Israel: The LORD our God, the LORD is one.
Therefore in Christian theology God is declared to be one as in Judaism. However, due to the the myriad of descriptions of Jesus and his relation to God, early church Fathers trying to make sense of said descriptions therefore formulated the Athanasian Creed defining God as is revealed in the New Testament. If you want, you can read it in full in the attached link, but to paraphrase, it states that the one God is not one in the strictest sense, but is triune (what is known as the Trinity).
What we call God in fact subsists of three persons -- the Father, Son and Holy Spirit. Their being of one lies in their shared godly substance (i.e their nature/genus). What follows, is that the Father is God, the Son is God, the Holy Spirit is God, but the Father is not the Son, nor is the Son the Father, the Father is not the Holy Spirit, nor is the Holy Spirit the Father, and the Son is not the Holy Spirit, nor the Holy Spirit the Son. The persons of the Trinity also share a close-knit relationship and co-dependency on each other.
The concept of the Trinity is illustrated in this picture:
As such, you can pray to either the person of the Son, the Father, or the Holy Spirit and still be praying to the same "one God" in Trinitarian belief. To me, the idea of one God seems to be defied the moment you speak of a multiplicity of persons instead of one.
When I think of a monotheistic God, I think of one person of one substance, rather than 3 different persons of one substance. You and me are different, because what characterizes our distinction and separate us from one another is the independence of our minds. If we were both under the control of one mind, it could be said that we are still the same person. Likewise conjoined twins who belong to the same body are distinct persons because it is theirs mind, their consciousness and their ability to think that defines their distinction from one another. The moment you have more than one person involved it logically follows that you have more than one human involved.
As such, when you pray to 3 different recipient persons who are all God, are you really praying to one God instead of three Gods? Can the the Trinity be logically justified as the belief in one God?