Correct.

And all those who had believed were together and had all things in common;  Acts 2:44 (NAS)

Belief in Jesus Christ and the gospel is a key ingredient for a person to become a Christian.  Jesus said in John 8:24 "...unless you believe that I AM, you will die in your sins."  In Mark 1:15 Jesus said "the kingdom of God is at hand.  Repent and believe in the gospel." 

Belief as the basis for our faith and obedience:

Jesus said in Mark 16:15-16:

And He said to them, "Go into all the world and preach the gospel to all creation. ¹⁶ "He who has believed and has been baptized shall be saved; but he who has disbelieved shall be condemned." Mark 16:15-16

If a person does not believe, it won't matter how good that person is...or the works that he or she does.  If a person does not believe, he or she "shall be condemned" and will "die in their sins."  However, a person who truly believes in Jesus and His promises, will do those things that Jesus says:

"Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls... And the Lord added to the church daily such as should be saved." Acts 2:41,47 (KJV)

Is it possible to believe in vain?

Not all that heard Peter's words in Jerusalem believed.  Some people may have believed in part, but chose not to repent or to be baptized for the remission of sins.  Acts 2:41-47 only talks of those who gladly received his word and were baptized. 

There are many who believe or claim to believe in Jesus...who never decide to follow His teachings.  James 2:19 says that "even the demons believe (in God)...and shudder."  Consider the following scriptures:

"For it is time for judgment to begin with the household of God; and if it begins with us first, what will be the outcome for those who do not obey the gospel of God? And if it is with difficulty that the righteous is saved, what will become of the godless man and the sinner?" 1 Peter 4:17-18 (NAS)

"...by which also you are saved, if you hold fast the word which I preached to you, unless you believed in vain." 1 Corinthians 15:2 (NAS)

"Nevertheless many even of the rulers believed in Him, but because of the Pharisees they were not confessing Him, lest they should be put out of the synagogue; for they loved the approval of men rather than the approval of God." John 12:42-43 (NAS)

"You believe that God is one. You do well; the demons also believe, and shudder."  James 2:19 (NAS)

Jesus said in Mark 16:16 "He who has believed and has been baptized shall be saved; but he who has disbelieved shall be condemned." Mark 16:16 (NAS)

What about those who reject the word?

Before Jesus died on the cross, John the baptist was preaching a baptism of repentance preparing the way for Jesus Christ. Some that heard John's message gladly accepted it, however, others decided not to be baptized with John's baptism:

"And when all the people and the tax-gatherers heard this, they acknowledged God's justice, having been baptized with the baptism of John. But the Pharisees and the lawyers rejected God's purpose for themselves, not having been baptized by John."  Luke 7:29-30 (NAS)

The Believers or Disciples were later called "Christians"

During Jesus' ministry, the believers were also called "disciples" (from the Greek word mathētēs, which means "learners"). Later on when Paul and Barnabas were together in Antioch (see Acts 11:26) it says "...the disciples were first called Christians in Antioch."

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