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Because Scripture teaches what it is to be saved. If we repent and believe, we are saved. Those are the elect. Those who don’t arent. It’s really not hard.

How does one know that he believes what is necessary to believe or that he has truly repented?

How do you know that your belief is not false or that your repentance is not based out of fear of hell or hope of heaven instead of a changed heart?

Much is made here about the importance of having correct doctrine and how there are "false conversions". The Arminian says that God chooses those who choose him, and the Calvinist claims that men only choose God because God has chosen them. In a sense I think it can be argued that both are right. Both you and Dr. E seem to be arguing that repentance and belief are evidence of salvation and that we can rest on that repentance and belief. I believe that too.

But then there are many who proclaim both belief and repentance who have doctrines which are diametrically opposed to what you or I believe and they are as sincere in their beliefs as you or I and are as contrite in their repentance as you or I. How can they be assured that their belief and repentance is evidence of their election if their beliefs are not exactly on point with yours? How can they know that their belief is not a product of their reprobate minds deceiving them or a product of a renewed heart given to them in order to make them repent and believe?

It is hard Gamecock. It's not just as simple as you say. If Calvinism is true to the core, then there are millions upon millions of people who have repented and believe (as they understand those terms) who were never intended to either repent or believe (as you understand those terms).

Is there a simple answer? Is there a "test" to determine if you are elect or if you are merely deceived?

And if you are deceived, is there a remedy, or are you hopelessly and forever lost?

“If Calvinism is true to the core, then there are millions upon millions of people who have repented and believe (as they understand those terms) who were never intended to either repent or believe (as you understand those terms).”

No, those people repented of and believed in the wrong things exactly as they were intended to repent of and believe in. Thus your statement is incoherent.