Me discrete versus me continuum arguments

Is the "Me" or "self" concept discrete or is it a continuum type of concept? A discrete concept is like true or false. In computers it is O or 1. There is no in between in usual computer calculations that why calculators give exact answers to mathematical calculations. The color red is a continuum like concept. There are many different colors that can be called red that are different from each other and they can be so closely alike that the eye can not tell the difference. The color red is due to the frequency of light that is not a discrete concept. One way to look at a discrete concept versus a continuum like concept is the difference between types of numbers. The difference between natural numbers 0 and 1 is discrete. But all of the real numbers between 0 and 1 form a continuum. There are no natural numbers between 0 and 1. But there are a real infinite amount of real numbers between 0 an 1 such as the series 1/2 1/3 1/4..... Between any two different real numbers there are an infinite amount of number not equal to each other.

A continuum concept does not have to have an infinite amount of variation between then, but there has to be more variations than the two extremes as in true or false. A statement can be partially true and partially false.

When a statement like "A replica of me is not me." is made it appears to be making the "self" or "me" concept out to be discrete. There is no room for anything in between the two extremes. Many concepts can be made to appear to be discrete. For example, "It is either red or it is not." "Either you are alive or you are not." "Either you like bananas or you don't." Often making something as discrete is a way to simply the situation. But with increasing knowledge discrete cases actually become more complex where there are actually in between cases. For example, it can be defined that any frequencies of light between x an y define the color red. But people will see red when the frequencies are out side of this range. Because of changes in the body the same person could see red with one frequency sometimes and not at other times.

How do we know that the "self" or "me" concept is actually discrete and not a continuum concept? The body seems to be discrete and the me concept is frequently based on the body. But is the body actually discrete? It is constantly changing in the space and time that it exist in and the matter that it is made of. Maybe more importantly the structure and functioning of the body is constantly changing. Making the body something discrete is making an arbitrary definition on a actual continuum concept thing called a body. If you freeze the body in space and time then there is more clearly a singular unique object yet it is still passing through space and time. The problem is it takes change in the body to produce consciousness. The most important part of you is being conscious. What about the "me" or "self" is then discrete besides being defined that way?

A cidentireplica may not be me but it is closer to being me than the most every other person that is not a cidentireplica of me. A cidentireplica thinks that it is me. It thinks the same thoughts, has the same memories, emotions, feelings, abilities, skills, knowledge, loves, hates, every conscious thing about a cidentireplica including its ixperiencitness is exactly like me as long as it is a cidentireplica of me. No matter how the cidentireplica is made these will be its attributes. No matter how it diverges when it was a cidentireplica it was exactly consciously like me at that section in my life.

The me concept is not well defined. When is the same body not me? When is a restored body me? When is a restored body of me just a cidentireplica of me and not the original.