Faith, Belief & Trust

"Keep the faith" is a popular phrase we hear, most times very casually spoken like "hey, hello, and see ya!" What does it really mean to "keep the faith, or have faith?  I have been wondering to myself lately what really is the difference between; faith, belief and trust.
Faith is believing the truth, for faith to be faith we must have a reason to believe. In 1 John 5:4 "For everyone born of God overcomes the world. This is the victory that has overcome the world, our faith."
Belief is an element of faith but not the whole. Trust is almost the inverse of faith, and the Lord requires it as well as faith at the same time. It is believing in spite of the evidence at hand.
This is one area we all can come together and agree on and each of us have dealt with these truths and topics daily, weekly or for a lifetime. Faith is a strong belief in someone or something without logical proof.
Trust is a firm reliance on the character or integrity of another person. Have you heard others say or have you yourself said "I have faith that you will do the right thing", or "I will keep having faith it will work out, regardless of how it seems to be." I myself say that, we all want to have hope! In Hebrews 11:1 it says "Now faith is the assurance of things hoped for, the conviction of things not seen."
We need to know what we believe in before we can claim to have faith. We need to hold on to actively trusting, and believe in what convicts our hearts.