Even the "New Catholic Encyclopedia On Line", admits that:

"In scripture there is as yet no single term by which the three Divine Persons are denoted together" 

However, in the first chapter of the Gospel of John, we are told about TWO BEINGS that co-existed before the material universe was created: 

"In the beginning was the Word ['Logos'- Greek, meaning Spokesman] and the Word was with God ['Theos'- The God] and the word was [a] god ['divine'- God like].  He was in the beginning with [The] God; all things were made through him and without him was not anything made that was made." Jn:1-3

As this scripture continues, we are told that the Word was made flesh and dwelt among us, as Jesus Christ our Savior. 
So 'God' (Elohim in Hebrew - a UNIPLURAL WORD that means MORE THAN ONE) - is a word that describes a family of two God beings: 
The Logos - God's spokesman (one divine personage of the God family) 
And Theos - "The God" - (the head of the God family). 
These two beings, who have no beginning of time nor end of days, comprise The God Family. 
It is made obvious by omission, that there was not a 3rd personage that existed with these beings in the beginning or John would have undoubtedly mentioned him. 
Yet, though not mentioned in the context of a personage, it is clear that this spirit existed then, since the Logos created the universe by IT. 
The Word speaks - and God's power (the Holy Spirit) emanates from Him to accomplish God's will. 
I suggest that a quick browsing of the salutations in the New Testament epistles will reveal no greeting to this supposed 3rd personage of the Godhead.  The reason for this is quite simple; the Holy Spirit is not a personage; it is, as scripture reveals - 
The operative Power of God. 

Luke 6:19 and 8:46 literally states this: 

"And all the crowd sought to touch him, for power came forth from him and healed them all". Lk 6:19 

"But Jesus said, 'Some one touched me; for I perceive that power has gone forth from me.'"  Luke 8:46 

What came forth from him?
POWER! 
By what means does God do all things, whether it's HEALING, CASTING OUT DEMONS, RAISING THE DEAD, PROPHESYING, etc? 
By the HOLY SPIRIT! 
The HOLY SPIRIT is the POWER OF GOD. 
Could it be any clearer than that? 
Now notice what Jesus says in Luke 11:13 about where this power to do miracles comes from: 

"...how much more will the heavenly Father give the Holy Spirit to those who ask him."  Luke 11:13

We know that all things are accomplished through the Holy Spirit, yet Jesus says that his Father gives Him the ability (or power) to do it, not some non-existent Ghost: 

"...the Son can do nothing of his own accord, but only what he sees the Father doing; for whatever He does the Son also does the same..."  Jn 5:19

It does not state anywhere in scripture that there is a trinity of co-equal beings, or that the Holy Spirit is a personage of the Godhead as traditional churches teach. 
In fact, upon unbiased investigation scripture only disproves this erroneous belief, not supports it. 
Jesus himself makes it known that he does not consider himself as a co-equal to His Father: 

"THE FATHER IS GREATER THAN I ... I do as the Father has commanded me..."   John 14:28

He also makes it clear that THE FATHER IS GREATEST OF ALL, even greater than the Holy Spirit, if IT were a being.

"MY FATHER, who has given them to me, is GREATER THAN ALL, and no one is able to snatch them out of the Father's hand.  I AND THE FATHER ARE ONE."  John 10:29

Notice - 
Jesus also says here that, "I and the FATHER are ONE". 
If there is a trinity, why didn't He say I, the Father and the Holy Spirit are One - or are Three, for that matter? 
Look also at Mt 19:17 - Jesus says:

"Why callest thou me good?  There is none good but ONE, that is, GOD."

Here, Jesus excludes himself (the second being of the Godhead) as being worthy of comparison to His Father, saying that only ONE (not, two other beings) is good. 
Again He fails to so much as mention, let alone describe as "good", the supposed 3rd God being. 
So we have determined scripturally that Christ's own words establish that the FATHER is the GREATEST of the GODHEAD, which contradicts the traditionalist's contention that the Godhead is comprised of three co-equal beings. 

We also know that Jesus was conceived by the Holy Spirit - 

"Joseph, son of David, do not fear to take Mary your wife, for that which is conceived in her is of the Holy Spirit..."  Mt 1:20

Yet, throughout the New Testament Jesus refers to God as His Father.  If the Holy Spirit were a person - especially the being that actually conceived him, why didn't Jesus refer to him as His Father. 
Again, the explanation is simple. 
Jesus does not refer to the Holy Spirit as "His Father" -
For the same reason He didn't include IT in His declaration that "He and His Father are one"
Or that "only one is good" - 
Because IT is not a being, IT is, as scripture has proven, the POWER OF GOD - 
The Holy Spirit is also described as something that must be renewed (2Cor 4:16), can be quenched (1Thes 5:19) and is poured out (Acts 2:17). 
These are not characteristics of a person. 
There are several scriptures that many who are deceived or grossly misinformed, use to justify this erroneous teaching - 
1John 5:7 and part of line eight for example were added in the Latin Vulgate centuries after the original epistle was written: 

["For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.] and there are the three that bear witness [in earth], the Spirit, and the water, and the blood; and these three agree in one" 1John 5:7-8 

The words in brackets were added by the Roman church to give validity to their belief in a Trinity that even the Catholic encyclopedia admits there is no scriptural evidence of. 
Matthew 28:19, which also seems to lend credibility to the trinity doctrine, is merely a mistranslation:

"Go ye therefore, and teach all nations, baptizing them [in the name of] the Father, and of the Son, and of the Holy Ghost..." Mt 28:19 

Within this century, Greek manuscripts were discovered dating back to Apostolic times, that have shed new light on how this scripture should be correctly translated. 
According to J. Moulton and G. Milligan in their book, "The Vocabulary of The Greek Testament", the words, "in the name of" should actually read, "into the possession of". It was found that this phrase was actually an accounting term that was commonly used during this time period and always connotes possession. 
It does not in any way personify the Holy Spirit. 
Put simply, we are baptized into the possession of the Family and power of God. 
Even John 14, which many use as proof of this non-existent 3rd personage, is not proof at all - look at John 14:16-17: 

"...and he will give you another Counselor to be with you forever, even the Spirit of truth, whom the world cannot receive, because it neither sees [him] nor knows [him]; you know [him], for [he] dwells with you, and will be in you." 

Here, talking about the Paraclete (Counselor/Comforter) or Holy Spirit that GOD will send to DWELL WITHIN US, the words in brackets once again make clear that he is not referring to a personage. 
These verses appear in the original Greek text as such: 

"...and he will give you another Counselor to be with you forever, even the spirit of truth, whom the world cannot receive, because IT neither sees IT nor knows IT; you know IT  for IT DWELLS WITH YOU, and will be in you." 

So the Holy Spirit that God SENDS TO DWELL IN US, John refers to as an IT, not a HE. 
Later in Jn 14:26, he refers to the Spirit as that one WHICH, (not who) the Father will send in my name. 
Here the Holy Spirit is referred to as "that one" - 
In several other places the Paraclete or Comforter is referred to as He. 
However these usages are metaphorical personifications as exists in all forms of literary expression. 
But if the Holy Spirit were a person, the word "IT", WOULD NEVER EVER be used to describe a being of the GODHEAD, as in fact, we have just seen in Jn 14:16-17. 
Could you imagine ever referring to the Father or Christ - as "IT"?! 
In Mt 12:22 - Jesus was seen casting out demons.  Matthew 12:28 tells us by what power He did this - 

"But if it is by the Spirit of God that I cast out demons..." 

As this quote again confirms, he did this by the Holy Spirit. 
But notice, He still credits Himself, and not a third being of the Godhead, for doing this.

"... I cast out demons" -

Not - HE (a 3rd God being) cast out demons -
But Jesus, by God's authority, using His Holy Power, did.
Finally, if God gave one of his prophets a vision of the Great Throne of God in Heaven, wouldn't you expect to find the 3rd personage sharing his throne as we know Christ does? 
Well in the book of Revelation John in fact describes just such a vision. 
Who did he describe as being in Heaven? 
First of all: 

"one seated on the throne"  Rev 4:2 

Then: 

"And between the throne and the four living creatures and among the elders, I saw a Lamb, as though it had been slain, with seven horns and with seven eyes, which are the seven spirits of God [angels - Zech 1:10, Zech 4:10, Heb 1:14] sent out into all the earth..."  Rev 5:6 

So we see: 
One (the Father) on the throne. 
Four living creatures. 
Elders. 
And Jesus (the Lamb that was slain). 
BUT AGAIN THE HOLY SPIRIT IS NOT MENTIONED. 
Why? 
Because as scripture has proven this supposed 3rd personage of the Godhead does not exist. 
The most fundamental of all traditional Christian doctrines - 
The holy trinity - 
Is just one of many paganistic beliefs and practices that have unfortunately become part of today's accepted mainstream Christian teachings.