The word translated faith is found in the Greek lexicon of the Strong’s Exhaustive Concordance and is defined as follows: #4102; pistis; persuasion, i.e. credence; moral conviction (of religious truth, or the truthfulness of God or a religious teacher), especially reliance upon Christ for salvation; abstractly, constancy in such profession; by extension, the system of religious (Gospel) truth itself:--assurance, belief, believe, faith, fidelity.
The word translated believe is from the greek word pisteuō which means "to have faith (in, upon, or with respect to, a person or thing), that is, credit; by implication to entrust (especially one’s spiritual well being to Christ)."
The word "believe" can describe mere "mental assent" (James 2:19) or also include "trust and reliance" (Acts 16:31). The Greek words for "pistis" and "pisteuo" are two forms of the same word. "Pistis" is the noun form, "pisteuo" is the verb form. Nothing in the root meaning of either word carries any concept of works. If you believe/have faith in Christ for salvation, then you are trusting in Him alone to save you. Authentic belief/faith results in actions appropriate to the belief - but the actions are NOT INHERENT in the belief. All genuine believers are fruitful, but not all are equally fruitful (Matthew 13:23).
Jesus goes into great detail to warn about those who are convinced they had "Faith" but refused to trust Jesus enough to follow His Instructions.
Matt. 7:22 Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works?
23 And then will I profess unto them, I never knew you: depart from me,
ye that work iniquity.
These "Believers" had fruits as you said all genuine believes have. They were also convinced in their mind that they were "Saved". They taught in Christ's name, surely they claimed"Belief" in Jesus. Yet, they were rejected from His Kingdom.
Why? Because of their "WORKS". Their "Works" showed who they really had "faith" in, who they really trusted. Had they truly believed in the Jesus of the Bible, they would have followed His teaching.
titus 1:16 They profess that they know God; but in works they deny
him, being abominable, and
disobedient,
and unto every good work reprobate.
Jesus warned that "MANY" would take this broad "Path". He said to "Strive to enter" (Work) into a different path.
34 And when he had called the people
unto him with his disciples also, he said unto them,
Whosoever will come after me,
let him deny himself, and
take up his cross,
and follow me. ( All Works)
15 If ye love me, keep my commandments. (Works)
16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;
17 Even the Spirit of truth;
whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
John 8:
31 Then said Jesus to those Jews which believed on him,
If ye continue in
my word,( Works)
then are ye my disciples indeed;
32 And ye shall know the truth, and the truth shall make you free.
Rom. 11:
20 Well;
because of unbelief they were broken off, and thou standest
by faith. Be not highminded, but fear:
But they all thought they did believe Dan. They were "convinced" that they were "Genuine believers", God's People. They had "fruits", some more than others. So why did Jesus say He rejected them?
Was it not because they omitted parts of His Instructions? Isn't that the reason why they were rejected? Wasn't that the "fruit" that allowed us to see their true faith?
23 Woe unto you, scribes and Pharisees, hypocrites! for ye pay tithe of mint and anise and cummin,
and have omitted the weightier matters of the law,(God's instructions)
judgment, mercy, and faith: these ought ye to have done, and not to leave the other undone.
So even though they claimed God as their savior, and they claimed to have "Faith" "Belief" in Him, they were deceiving themselves because if they had truly loved, trusted, had Faith in Him, they would have done as He instructed as did Abraham.
Paul is using them as a tool of warning for us.
21 For if God spared not the natural branches,
take heed lest he also spare not thee.
22 Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness,
if thou continue in
his goodness: (Works)
otherwise thou also shalt be cut off.
As it is written;
8 For by grace are ye saved
through faith; and that not of yourselves:
it is the gift of God:
9 Not of (mans) works,
lest any man should boast.
10 For we are his workmanship, created in Christ Jesus
unto good works,
which God hath before ordained that we should walk in them.
So to conclude, those who have true "Faith" in Jesus with trust Him enough to do as He says. We will deny our thoughts, take up our individuality, and follow Him. Not the religious traditions of man as "Many" did in Christ's time. But we will submit our self to Him and HIS Ways.
"IF" we do these things He is faithful to give us what we need to endure all the religious snares and traps out there. But if we refuse to believe in Him enough to follow His instructions, then because of this "unbelief" we will also be cut of as the Mainstream Preachers and those who followed their teaching were cut off in Christ's time.